If additional memory for your computer sells for $109.99 with a $10.00 mail-in rebate, an envelope costs $0.35 and a 'forever' postage stamp costs $0.41,then the cost after all the rebates will be $100.75.
Given that additional memory for your computer sells for $109.99 with a $10.00 mail-in rebate, an envelope costs $0.35 and a 'forever' postage stamp costs $0.41.
We are required to find the cost after all the rebates and envelopes provided.
The cost can be calculated as under:
Cost=109.99-10.00+0.35+0.41
=$100.75
Hence if additional memory for your computer sells for $109.99 with a $10.00 mail-in rebate, an envelope costs $0.35 and a 'forever' postage stamp costs $0.41,then the cost after all the rebates will be $100.75.
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Marco bought 12 roses for
$48. What was the original
cost of EACH rose before
the discount? Set up an
equation and solve to
answer this question
Super Saver
DEALS! Get $2
off each rose
when you buy 12
or more roses
Marco bought 12 roses for $48. Each rose was originally $4 before the discount, and Super Saver Get $2 off each rose when you buy 12 or more roses each rose is $6.
How to calculate discount?The discount formula is as follows: Discount = Marked Price - Selling Price. OR. Formula for Discount Percentage = Marked Price Discount Rate A 10% discount can be calculated in two steps: Step 1 is to convert your percentage to a decimal using the formula 10 / 100 = 0.1. As a decimal, 10% equals 0.1. Step 2 is to multiply your original price by the decimal you chose. The sweaters were originally priced at $80. The store would like to offer a 15% discount on the sweaters. The company converts 15% to the decimal 0.15 to calculate the discount. The result is a figure of $12 after multiplying 0.15 by the original price of $80.Therefore,
Marco bought 12 roses for $48. Each rose was originally $4 before the discount.
∴ 48/12 = $4 and,
Super Saver Get $2 off each rose when you buy 12 or more roses
each rose is $6.
∴ 12/2 = $6
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Identify the property used in each step of solving the inequality 7x+4 <46,
Step
7x+4 <46
7x <42
x <6
Answer:
1) Given
2) Subtraction Property of Inequalities
3) Division Property of Inequalities
Can’t find the correct answer pls help
Help mee pleasee!!
thank you <3
...................
For each system to the best description of a solution if applicable give the solution
System A
[tex]\begin{gathered} x-4y=4 \\ -x+4y+4=0 \end{gathered}[/tex]solve the first equation for x
[tex]x=4+4y[/tex]replace in the second equation
[tex]\begin{gathered} -(4+4y)+4y+4=0 \\ -4-4y+4y+4=0 \\ 0=0 \end{gathered}[/tex]The system has infinitely many solutions, They must satisfy the following equation
[tex]\begin{gathered} x-4y=4 \\ -4y=4-x \\ y=\frac{4}{-4}-\frac{x}{-4} \\ y=\frac{x}{4}-1 \end{gathered}[/tex]System B
[tex]\begin{gathered} x-2y=6 \\ -x+2y=6 \end{gathered}[/tex]solve for x for the first equation
[tex]x=6+2y[/tex]replace in the second equation
[tex]\begin{gathered} -(6+2y)+2y=6 \\ -6-2y+2y=6 \\ -6=6 \end{gathered}[/tex]The system has no solution.
Lashonda, Josh, and Brian sent a total of 90 text messages during the weekend, Lashonda sent 10 more messages than Josh. Brian sent 2 times as manymessages as Josh. How many messages did they each send?Number of text messages Lashonda sent:Number of text messages Josh sent:Number of text messages Brian sent:
Defining:
Number of messages of Lashonda = L
Number of messages of Josh = J
Number of messages of Brian = B
We know that:
L+J+B=90 (Equation 1)
We also know:
L = J+10 (Equation 2)
B=2J (Equation 3)
Now, we can substitue the values for L and B in the first equation
L+J+B=90
J+10 + J + 2J = 90
4J=90-10
4J=80
J=80/4
J=20
Since you found how many messages Josh sent, we can return to Equation 2 and 3:
L = J+10
L = 20 + 10
L = 30
B=2J
B=2*20
B=40
ANSWER:
Number of text messages Lashonda sent: 30
Number of text messages Josh sent: 20
Number of text messages Brian sent: 40
An aerospace company has submitted bids on two separate federal government defense contracts. The company president believes that there is a 45% probability of winning the first contract. If they win the first contract, the probability of winning the second is 75%. However, if they lose the first contract, the president thinks that the probability of winning the second contract decreases to 52%.
1. The probability that they win both contract will be 23.4%.
How to calculate the probability?It should be noted that probability simply means the likelihood that an event will occur.
The probability of winning the contract will be:
= Probability of A winning × Probability of B winning
= 45% × 52%
= 0.45 × 0.52
= 0.234
= 23.4%
The probability is 23.4%
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7.4.PS-15 Question Help Juanita has 3 rectangular cards that are 7 inches by 8 inches. How can she arrange the cards, without overlapping, to make one larger polygon with the smallest possible perimeter? How will the area of the polygon compare to the combined area of the 3 cards? The perimeter of the polygon is 58 in. (Type a whole number.) How will the area of the polygon compare to the combined area of the 3 cards? O A. The areas will be equal. OB. The area of the polygon will be greater than the combined area of the cards. OC. The area of the polygon will be less than the combined area of the cards. OD. This is impossible to determine with the given information. Click to select your answer and then click Check Answer. All parts showing Clear All Check Answer Review progress Question 8 of 10 Back Next →
Since there is no overlapping the area of the polygon must be equal to the combined area of the cards.
The diameters of bolts produced in a machine shop are normally distributed with a mean of 5.48 millimeters and a standard deviation of 0.07 millimeters. Find the two diameters that separate the top 3% and the bottom 3%. These diameters could serve as limits used to identify which bolts should be rejected. Round your answer to the nearest hundredth, if necessary.
The two diameters that separate the top 35 from the bottom 35 in the normal distribution are 5.35 mm and 5.61 mm .
Normal distributions are crucial to statistics because they are widely used in the natural and social sciences to represent real-valued covariates whose distributions are unknown.
Some of their significance comes from the main limit theorem. This claim states that, in some cases, the average of many samples (observations) of a stochastic process with limited mean and variance constitutes itself as a random variable, whose distribution tends to become more normal as the number of samples increases. Because of this, the distributions of physical quantities, like misspecification, which are thought to be the consequence of hundreds of distinct processes, are frequently close to normal.First we will find the bottom 3% such that P(X ≤ x) = 0.03
⇒ [tex]P(\frac{X-5.48}{0.07}\leq \frac{x-5.48}{0.07} )=0.03[/tex]
⇒[tex]P(Z\leq \frac{x-5.48}{0.07} )=0.03[/tex]
Now we will use the normal table to calculate the corresponding z-score.
[tex]\frac{x-5.48}{0.07} =-1.88\\\\\implies x = 5.348[/tex]
Now we will find the same for the top part of the distribution.
[tex]P(\frac{X-5.48}{0.07}\leq \frac{x-5.48}{0.07} )=0.97\\\\\implies P(Z\leq \frac{x-5.48}{0.07} )=0.97[/tex]
Now we will use the normal table to calculate the corresponding z-score.
[tex]\frac{x-5.48}{0.07} =1.88\\\\\implies x = 5.612[/tex]
The two diameters that separate the top 35 from the bottom 35 in the normal distribution are 5.35 mm and 5.61 mm .
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Solve the word problem. Show all the steps.
Two numbers add to 39. One number is 9 less than 7 times the other. What are the numbers?
The numbers represented by the word problems are 33 and 6
How to determine the solution to the word problem?The statements in the question are:
Two numbers add to 39. One number is 9 less than 7 times the other.Let the numbers in the expressions be x and y
So, we have
x + y = 39
x = 7y - 9
Substitute x = 7y - 9 in the equation x + y = 39
So, we have
7y - 9 + y = 39
Evaluate the like terms
8y = 48
Divide both sides by y
y = 6
Substitute y = 6 in x + y = 39
x + 6 = 39
Evaluate the like terms
So, we have
x = 33
Hence, the numbers are 33 and 6
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Hanson is fixing up his home and must spend less than $6,900 to hire carpenters and painters. Carpenters charge $41 per hour and painters charge $16 per hour.
Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.
A) The inequality for the situation is 41x + 16y < 6900
B) The painter can work less than 97 hours without exceeding the budget of Hanson.
Given,
The total money spend by Hanson = < $6900
The charge for carpenters = $41 per hour
The charge for painters = $16 per hour
A) We have to find an inequality for this situation.
Lets take,
Carpenters working hours = x
Painters working hours = y
So, the inequality will be like:
41x + 16y < 6900
B) Now, we have to find the number of hours the painter can work without exceeding his budget if he hires carpenter.
Carpenters working hours = 50
Then, the charge will be = 50 × 41 = 2050
Then,
6900 - 2050 = 4850
The balance amount will be less than 4850.
So, the working hours of painter:
y < 4850 / 50
y < 97
That is, the painter can work less than 97 hours without exceeding the budget of Hanson.
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The question is incomplete. Completed question is given below:
Hanson is fixing up his home and must spend less than $6,900 to hire carpenters and painters. Carpenters charge$41 per hour and painters charge $16 per hour.
Part A: Write an inequality to represent the situation.
Part B: If he hires a carpenter for 50 hours, what is the maximum number of hours the painter can work without exceeding his budget?
For the following exercises, evaluate the function f at the indicated values.
a. f(-3) b. f(2) c. f(-a) d. -f(a)
4. f(x)=2x-5
5. f(x)=−5x²+2x−1
6. f(x)=x-1-x+1
After we evaluate the function f at the indicated values the results are
a. (4) −11, (5) −52, (6) 0
b. (4) -1, (5) −17, (6) -5
c. (4) −2a−5, (5) −5a² −2a−1, (6) −3+a
d. (4) −2a+5, (5) 5a² −2a+1, (6) 3+a
What is function?A relation in which there is only one possible pairing of each x and each y is called a function. It should be noted that while the reverse is true, the same y can be paired with different x. Vertical and horizontal lines are the only types of linear equations that are not functions.
Lets evaluate the function a. f(-3)
4. f(-3) = 2(-3)-5
= −11
5. f(-3) = −5(-3)²+2(-3)−1
= −52
6. f(-3) = -3-1-(-3)+1
= 0
Lets evaluate the function b. f(2)
4. f(2) = 2(2)-5
= −1
5. f(2) = −5(2)²+2(2)−1
= −17
6. f(2) = -3-1-(2)+1
= −5
Lets evaluate the function c. f(-a)
4. f(-a) = 2(-a)-5
= −2a−5
5. f(-a) = −5(-a)²+2(-a)−1
= −5a² −2a−1
6. f(-a) = -3-1-(-a)+1
= −3+a
Lets evaluate the function d. -f(a)
4. -f(a) = -(2(a)-5)
= −2a+5
5. -f(a) = -(−5(a)²+2(a)−1)
= 5a² −2a+1
6. -f(a) = -(-3-1-(a)+1)
= 3+a
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What is the simplified form: (8m + 1)^2
Answer
(8m + 1)^2 = (8m + 1)² = 64m² + 16m + 1
Explanation
The question simply wants us to simplify the expression
(8m + 1)^2
= (8m + 1)²
= (8m + 1) (8m + 1)
= 8m (8m + 1) + 1 (8m + 1)
= 64m² + 8m + 8m + 1
= 64m² + 16m + 1
Hope this Helps!!!
URGENT!!) Which of the following served as the primary route for transporting cotton to Georgia's only sea port? (5 points)
a
The Savannah River
b
The Chattahoochee River
c
The Oconee River
d
The Suwanee River
Answer:
Correct answer:
a. The Savannah River
Find the range and mean of each data set. Use your results to compare the two data sets.Set A:Set B:2 10 8 19 2314 16 15 17 16
Range of a Data Set :
The range of a set of data is the difference between the highest and lowest values in the set
MEAN :
The mean is the mathematical average of a set of two or more numbers
Set A: 2, 10, 8, 19, 23
Arrange the data of set A in ascending order;
Set A : 2, 8, 10, 19, 23
For range; the highest term is 23, lowers term is 2
Range = highest - lowest
Range = 23 - 2
Range = 21
for Mean; the sum of all entries divided by the total number of entries in data set.
In data A, total number of entries are : 5
[tex]\begin{gathered} \text{ Mean = }\frac{2+8+10+19+23}{5} \\ \text{Mean}=\frac{62}{5} \\ \text{Mean}=12.4 \end{gathered}[/tex]Thus, mean of set A is 12.4
Now, for set B;
Set B : 14 16 15 17 16
Arrange the elements of set B in the ascending order;
Set B : 14, 15, 16, 16, 17
For range; the highest term is 17, lowers term is 14
Range = highest - lowest
Range = 17-14
Range = 3
Thus, range of set B is 3
for mean of set B;
The sum of all entries divided by the total number of entries in data set.
In data B, total number of entries are : 5
[tex]\begin{gathered} \text{ Mean = }\frac{14+16+15+17+16}{5} \\ \text{Mean}=\frac{78}{5} \\ \text{Mean}=15.6 \end{gathered}[/tex]Thus, the mean for set B is 15.6
Answer : The mean of set A is 12.4 and range is 21
The mean of set B is 15.6 and range is 3
Pls help asap
Find the product of 5.3 x 10^12 and 5.12 x 10^9. Write the final answer in scientific notation.
2.7136 x 10^21
2.7136 x 10^22
27.136 x 10^21
27.136 x 10^22
Answer:
B. 2.7136 x 10^22
Step-by-step explanation:
Hope this helps :))
A company has determined that the demand function for a certain couch is given by
= 2700 − 0.75, where p is the price per couch, and x is the number of couches sold. The fixed costs associated with producing a line of couches is $760,000, and each couch costs $360 to make. Determine how many couches should be manufactured and sold in order to maximize profit. Start by finding functions to represent the revenue and the total cost, then find a function for profit
The number of couches manufactured and sold in order to maximise the profit is 1560.
The demand function will be
p = 2700 - 0.75x
Here p = price per couch and x = number of couch
Total Fixed cost = $760000
Variable cost per couch = $360
Total cost = Fixed cost + variable cost
T(x) = 760000 + 360x
Revenue function will be
R(x) = Px
(2700 - 0.75x)x
2700x - 0.75x²
Since profit function = Pr(x)
Pr(x) = R(x) - T(x)
= 2700x - 0.75x² -760000 -360x
- 0.75x² + 2700x - 360x - 760000
For maximum profit
[tex]\frac{d}{dx}(Pr(x)) = 0[/tex]
[tex]\frac{d}{dx}[-0.75x^{2} + 2340x -760000 ] = 0[/tex]
-1.5x + 2340 = 0
x = 2340/1.5
x = 1560
The couches sold for maximum profit = 1560
Therefore, the number of couches manufactured and sold in order to maximise the profit is 1560.
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A linear function is shown on the graph
6
What is the domain of the function?
O(x10≤x≤4)
O(x10
Oy 12sy≤6)
0012
Question 1 (Answered)
MATHEMATICALLY we say
[tex]0 \leqslant x \leqslant 4[/tex]
THAT IS THE DOMAIN OF THE GRAPH
THAT IS THE DOMAIN OF THE GRAPHOPTION A IS THE ANSWER.
Among the following which is the best
example for unlike terms?
O8x, 9t
O 9x-2x
О 3р. 5р
All of the choices
Bea is asked to graph this system of equations: 8x - 6y= 3 -3y + 4x = 4 How many times will the lines intersect?
Given the system of equations:
8x - 6y = 3
-3y + 4x = 4
To find how many times the lines will intersect. let's solve the system of equation using substitution method.
8x - 6y = 3 ........................................1
-3y + 4x = 4 ......................................2
From equation 1, make x the subject:
8x - 6y = 3
8x = 3 + 6y
[tex]\begin{gathered} x=\frac{3}{8}+\frac{6}{8}y \\ \\ x=\frac{3}{8}+\frac{3}{4}y \end{gathered}[/tex][tex]\text{Substitute (}\frac{3}{8}+\frac{3}{4}y)\text{ for x in equation 2}[/tex]We have:
[tex]\begin{gathered} -3y+4(\frac{3}{8}+\frac{3}{4}y)=4 \\ \\ -3y+\frac{3}{2}+3y=4 \\ \\ \end{gathered}[/tex]Multiply through by 2 to eliminate the fraction:
[tex]\begin{gathered} -3y(2)+\frac{3}{2}(2)+3y(2)=4(2) \\ \\ -6y+3+6y=8 \end{gathered}[/tex][tex]\begin{gathered} -6y+6y=8-3 \\ \\ 0=5 \end{gathered}[/tex]Since we have 0 = 5, it means the system of equations has no solution.
Therefore, the lines will not intersect, because this system has no solution.
ANSWER:
A. The lines will not intersect, because this system has no solution.
Match the one-to-one functions with their inverse functions.
Matching the following function
What is a Function?
Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
The function of f^(-1)(x) = 5x is:
f(x)= x / 5
The function of f^(-1)(x) = x^3 / 2 is:
f(x)=3√2x
The function of f^(-1)(x) = x+10 is:
x - 10
The function of f^(-1)(x) = 3(x + 17) / 2 is:
(2x / 3) - 17
Hence, These are the Match of one-to-one functions with their inverse functions.
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"An orchestra of 120 players take 70 minutes to play Beethoven's 9th symphony," "How long would it take for 60 players to play the symphony?"Answer the question an explain*
We have that in 70 minutes 120 players of an orchestra play Beethoven's 9th symphony because it always lasts 70 minutes.
The lenght of a musical piece does not depend in the number of musicians playing it. The orchestra could have 2 violinists more or less and they still will play the same 70 minutes musical piece.
Then, an orchestra of 60 players would take the same 70 minutes to play Beethoven's 9th symphony.
Answer: 70 minutesConvert 63°F to degrees Celsius. If necessary, round your answer to the nearest tenth of a degree. Here are the formulas. 5 C== (F-32) F=-6 +32 5 63 PF - I c
The given temperature is 63 F
The formula for convert temperature into Degree C from Degree F.
[tex]C=\frac{5}{9}(F-32)[/tex]Substitute all the value in the above equation.
[tex]\begin{gathered} C=\frac{5}{9}(63-32) \\ C=\frac{5}{9}\times31 \\ C=17.22C \end{gathered}[/tex]The nearest tenth is 17degree C.
write the quadratic equation whose roots are -2 and 1 and whose leading coefficient is 4 using the letter x to represent the variable
The quadratic equation is y = 4. (x + 2)(x - 1).
Given,
The roots are -2 and 1 and whose leading coefficient is 4 using the letter x to represent the variable.
To Write the Quadratic Equation by using above given:
Now, According to the question:
Roots are -2 and 1
Leading Coefficient is = 4
Using Variable is = x
Formulate the equation of polynomial function is
y = 4. (x + 2)(x - 1)
Hence, The quadratic equation is y = 4. (x + 2)(x - 1).
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How do I solve the missing verticals angles for L2 and L3?
The vertical angle theorem states that two opposite angles that are formed when two lines intersect each other are always equal, graphically this looks like this:
Then, if we apply this theorem to the figure shown we can say that
[tex]\begin{gathered} L1=L3 \\ L2=L4 \end{gathered}[/tex]This means that:
[tex]\begin{gathered} L2=110.6 \\ L3=69.4 \end{gathered}[/tex]What is the slope of the line passing through the points (0, 5) and (4,2) ^ prime
[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{0}}} \implies \cfrac{ -3 }{ 4 } \implies {\Large \begin{array}{llll} - \cfrac{ 3 }{ 4 } \end{array}}[/tex]
The area of the triangle below is40 square meters. What is the length of the base?Express your answer as a fraction in simplest form.
Given the area of the triangle:
[tex]A=\frac{3}{40}m^2[/tex]You can identify in the figure provided in the exercise that the height of the triangle is:
[tex]h=\frac{1}{5}m[/tex]The area of a triangle can be calculated using this formula:
[tex]A=\frac{bh}{2}[/tex]Where "A" is the area, "b" is the base, and "h" is the height.
If you solve for "b", you obtain this formula:
[tex]\begin{gathered} 2A=bh \\ \\ b=\frac{2A}{h} \end{gathered}[/tex]Therefore, knowing the Area and the height of the triangle, you can substitute them into the formula and then evaluate, in order to find the length of its base:
[tex]b=\frac{(2)(\frac{3}{40})}{\frac{1}{5}}[/tex][tex]b=\frac{\frac{6}{40}^{}}{\frac{1}{5}}[/tex][tex]b=\frac{6\cdot5}{40\cdot1}[/tex][tex]b=\frac{30}{40}[/tex][tex]b=\frac{3}{4}m[/tex]Hence, the answer is:
[tex]b=\frac{3}{4}m[/tex]What is the approximate area of a clock face with a diameter of eight inches?
The area formula of a circle is :
[tex]A=\frac{1}{4}\pi D^2[/tex]From the problem, the diameter is 8 inches.
The area will be :
[tex]\begin{gathered} A=\frac{1}{4}\pi(8)^2 \\ A=50.27 \end{gathered}[/tex]The answer is 50.27 in^2
Hi, can you help me with this exercise please, Find the value of x. Round lengths of segments to the nearest tenth and angle measures to the nearest degree.
From the given figure , we will use the Sine function in order to find segment x .
Sin 70 ° = opposite /hypotaneus
Sin 70 ° =x /7
∴x = 7* Sin 70°
x = 6.5778
x ≈6.6 ...( rounded to the nearest 10 )
Write the equation of the line with the points (0, 2) and (4, 10) in standard form.
By definition, the of a line written in Standard form is:
[tex]Ax+By=C[/tex]Where "A", "B" and "C" are Integers ("A" is positive).
The Slope-Intercept form of the equation of a line is:
[tex]y=mx+b[/tex]Where "m" is the slope and "b" is the y-intercept.
You know that this line passes through these points:
[tex](0,2);(4,10)[/tex]By definition, the value of "x" is zero when the line intersects the y-axis. Then, you can identify that, in this case:
[tex]b=2[/tex]Now you can substitute the value of "b" and the coordinates of the second point into the following equation and solve for "m":
[tex]y=mx+b[/tex]Then, the slope of the line is:
[tex]\begin{gathered} 10=m(4)+2 \\ 10-2=4m \\ 8=4m \\ \\ \frac{8}{4}=m \\ \\ m=2 \end{gathered}[/tex]Therefore, the equation of this line in Slope-Intercept form is:
[tex]y=2x+2[/tex]To write it in Standard form, you can follow these steps:
- Subtract 2 from both sides of the equation:
[tex]\begin{gathered} y-(2)=2x+2-(2) \\ y-2=2x \\ \end{gathered}[/tex]- Subtract "y" from both sides of the equation:
[tex]\begin{gathered} y-2-(y)=2x-(y) \\ -2=2x-y \\ 2x-y=-2 \end{gathered}[/tex]The answer is:
[tex]2x-y=-2[/tex]Answer:
2x-y =-2
Step-by-step explanation:
To find the equation of the line in standard form, first, we need to find the slope
m = ( y2-y1)/(x2-x1)
m = (10-2)/(4-0)
= 8/4 = 2
Then we can use the slope intercept form
y = mx+b where m is the slope and y is the y-intercept
y = 2x +b
Using the y-intercept ( 0,2)
y = 2x +2
The standard form is Ax +By =C where A is a positive integer and B is an integer
Subtract 2x from each side
-2x +y = 2
Multiply each side by -1
2x-y =-2
