The factoring the equation (a + 1)² - 4b² we get (a+1+2b)(a+1-2b).
What is the factoring function of (a + 1)² - 4 b²?Given: (a + 1)² - 4b²
Apply Perfect Square Formula, and we get
(a + b)² = a² + 2 a b + b²
(a + 1)² = a² + 2a1+1²
= a² + 2a1 + 1² - 4 b²
simplifying the equation, we get
a² + 2a1 + 1² = a² + 2a + 1
= a² + 2a + 1 - 4b²
Factor, a² + 2a + 1 = (a + 1)²
= (a + 1)² - 4 b²
Simplify 4 b² = (2 b)²
= (a + 1)² - (2b)²
Apply the Difference of Two Squares Formula, and we get
x² - y² = (x + y)(x - y)
(a + 1)² - (2b)² = ((a + 1) + 2b)((a + 1) - 2 b)
simplifying the equation, we get
= ((a + 1) + 2b)(a + 1) - 2 b)
= (a + 1 + 2b)(a + 1 - 2b)
Therefore, the correct answer is (a+1+2b)(a+1-2b).
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the area of a piece of land is 4.08km^2. it is bought at a piece of $6000 per square km. calculate the total cost of the land, giving our answer to the nearest $100
Answer:
22480.000
Step-by-step explanation:
Cost of 1km²=6000
So,
Cost of 4.08km²=6000x4.08
=22480.000
I don't know what nearest $100 means tho maybe nearest hundredth but I'm not sure.
The total cost nearest 100 is = $22500.
What is area?Modern mathematics heavily relies on the concept of area. The area is the quantity that shows the amount of space occupied by a two-dimensional figure or shape or planar lamina in the plane. Simply put, the area is the amount of cloth or other material with the specified thickness needed to build a model of the form or the quantity of paint required to cover the shape's surface in a single layer, or "coat," of paint.
According to the given Information:Cost of 1km2 = 6000
So,
Cost of 4.08km2 = 6000 * 4.08
= 22480.000
Rounding off to 100;
Cost = 22500.00
Hence,
Total cost of the land nearest 100 is = $22500.
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Ben invests Nu 125,000 in a bank shares with a face value of Nu 100 but they are being sold at a premium of 25%. How many shares can he buy?
Answer:
This is your answer!
Step-by-step explanation:
40 POINTS AND BRAINLIEST!! Solve for x in the following equations..
a) 6x +3 +21
b) 15(x - 5) = 75
c) 3/4 x +5 = 26
Answer:
a) x = 3
b) x = 10
c) x = 28
Explanation:
a)
[tex]\sf 6x + 3 = 21[/tex]
collect term
[tex]\sf 6x = 21-3[/tex]
simplify
[tex]\sf 6x = 18[/tex]
divide both both sides by 6
[tex]\sf x = 3[/tex]
b)
[tex]\sf 15(x - 5) = 75[/tex]
distribute
[tex]\sf 15x - 75 = 75[/tex]
collect terms
[tex]\sf 15x = 75 + 75[/tex]
combine
[tex]\sf 15x = 150[/tex]
divide both sides by 15
[tex]\sf x = 10[/tex]
c)
[tex]\sf \frac{3}{4} x +5 = 26[/tex]
collect like terms
[tex]\sf \frac{3}{4} x = 26-5[/tex]
combine
[tex]\sf \frac{3}{4} x = 21[/tex]
cross multiply
[tex]\sf x = \frac{ 21 (4)}{3}[/tex]
simplify
[tex]\sf x =28[/tex]
Resolver por igualación
2x+3y=2
6x+12y=1
Answer:
[tex]x = 3.5[/tex]
[tex]y\approx1.666666667[/tex]
Step-by-step explanation:
To solve simultaneous equations, at least one of our variables must have the same coefficient. We can easily multiply the first equation by 4 to get 12y on both sides, so let's do that:
[tex]8x + 12y = 8[/tex]
No let's subtract the second equation from the first equation to get the third equation:
[tex]2x = 7[/tex]
Solve:
[tex]x = 3.5[/tex]
Now, we can substitute this value into one of the original equations - let's use the second one:
[tex]21 + 12y = 1[/tex]
Solve:
[tex]12y = - 20[/tex]
[tex]y = - \frac{ - 20}{12} = \frac{ - 10}{6} = - \frac{5}{3} \approx - 1.66666666667[/tex]
Solve the system of equations below by graphing. Write the solution as an ordered pair. y = −5x y = x − 6
Answer:
x=1 and y=−5
Step-by-step explanation:
Problem:
Solve y=−5x;y=x−6
Steps:
I will solve your system by substitution.
y=−5x;y=x−6
Step: Solve y=−5x for y:
Step: Substitute −5x for y in y=x−6:
y=x−6
−5x=x−6
−5x+−x=x−6+−x (Add -x to both sides)
−6x=−6
−6x/−6=−6/−6 (Divide both sides by -6)
x = 1
Step: Substitute 1 for x in y=−5x:
y=−5x
y=(−5)(1)
y=−5(Simplify both sides of the equation)
Answer:
x=1 and y=−5
Thank you,
Eddie
Help please !!!!!!! Need helppppp
Answer:
option c
Step-by-step explanation:
option c is a correct answer
giving brainliest to right answer tyy
Answer:
B
Step-by-step explanation:
Original form:
y=mx+b
m=slope
b=y interecept
By replacing those variables with the given we come up with the equation of:
y=3/2x-7
Answer:B
Step-by-step explanation:
Here are the scores of 18 students on a history test. 55, 57, 58, 61, 62, 66, 68, 68, 71, 75, 75, 78, 82, 83, 85, 86, 88, 89. Notice that the scores are ordered from least to greatest. Make a box-and-whisker plot for the data.
The box-and-whisker plot for the given data is given below:
A box and whisker plot is defined as a graphical method of displaying variation in a set of data.
The results of a history test taken by 18 students: 55, 57, 58, 61, 62, 66, 68, 68, 71, 75, 75, 78, 82, 83, 85, 86, 88, 89.
Take note of how the scores are listed from lowest to highest.
The median for the given data is 73.
The Lower Quartile and the Upper Quartile would be found after that.
These represent the lower and higher halves' medians.
Lower quartile = 61.75
Upper quartile = 83.5
Make a number line. Mark your median, quartiles, and smallest and largest values.
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I NEED ANSERS AND SOLUTIONS PLSS DUE TMR. NEED HELP
The solutions using the relevant theorems are:
13. x = −3 or x = 4
14. x = 12
15. x = 12
16. x = 1/2 or x = 4
17. x = 5
18. x = −1 or x = 6
What is the Triangle Midsegment Theorem?The midsegment of a triangle that joins two sides of a triangle divides the two sides proportionally based on the triangle midsegment theorem.
What is the Angle Bisector Theorem?
The angle bisector of a triangle, according to the angle bisector theorem divides the opposite angles sides in a proportional manner.
What is the Parallel Lines and Proportionality Theorem?The theorem states that when three or more lines that are parallel is cut across by two transversals, they are divided by the transversal proportionally.
13. Apply the angle bisector theorem:
x/3 = (x + 4)/(x + 2)
Cross multiply
x(x + 2) = 3(x + 4)
x² + 2x = 3x + 12
x² + 2x - 3x - 12 = 0
x² - x - 12 = 0
Factorize
x = −3 or x = 4
14. Apply the angle bisector theorem:
16/x = 12/9
x(12) = (16)(9)
12x = 144
x = 12
15. Apply the angle bisector theorem:
(x - 4)/6 = x/9
9(x - 4) = 6x
9x - 36 = 6x
9x - 6x = 36
3x = 36
x = 12
16. Apply the triangle midsegment theorem:
3x/(x + 4) = (x - 1)/(x - 2)
Cross multiply
3x/(x + 4) = (x - 1)/(x - 2)
(x - 1)(x + 4) = 3x(x - 2)
x² + 3x - 4 = 3x² - 6x
x² + 3x - 4 - 3x² + 6x = 0
-2x² + 9x - 4 = 0
Factorize
x = 1/2 or x = 4
17. Apply the Parallel Lines and Proportionality Theorem:
(x + 3)/(2x + 2) = (2x + 2)/(4x - 2)
Cross multiply
4x² + 10x - 6 = 4x² + 8x + 4
4x² + 10x - 6 - 4x² - 8x - 4 = 0
2x - 10 = 0
2x = 10
x = 5
18. Apply the angle bisector theorem:
(2x + 3)/x = (x + 4)/(x - 2)
Cross multiply
(2x + 3)(x - 2) = x(x + 4)
2x² - x - 6 = x² + 4x
2x² - x - 6 - x² - 4x = 0
x² - 5x - 6 = 0
Factorize
x = −1 or x = 6
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Area=
Help me please asap.
Thanks so much :)
The area of the given parallelogram is 8 square units
Area of a parallelogramA parallelogram is a 2 dimensional figure with 4 sides and angles. From the given diagram, the opposite sides are equal and the sum of the adjacent angles are supplementary
The formula for calculating the area of a parallelogram is expressed as:
A = base * height
From the given diagram
Base = (4, 0) = 4 units
Height. = (2, 0) = 2 units
Substitute the given values into the formula to have:
A = 4 units * 2 units
A = 8 square units
Hence the area of the given parallelogram is 8 square units
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What is the product of (5 m superscript negative 2 baseline) (2 m superscript negative 3 baseline)?
Answer:
A
Step-by-step explanation:
(4r-5r^2) - (r-2r^2)
Answer:[tex]3r-29r^2[/tex]
Step-by-step explanation:
The following Visual Image consists with the steps
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Determine if the following infinite series converges or diverges
Using limits, it is found that the infinite sequence converges, as the limit does not go to infinity.
How do we verify if a sequence converges of diverges?Suppose an infinity sequence defined by:
[tex]\sum_{k = 0}^{\infty} f(k)[/tex]
Then we have to calculate the following limit:
[tex]\lim_{k \rightarrow \infty} f(k)[/tex]
If the limit goes to infinity, the sequence diverges, otherwise it converges.
In this problem, the function that defines the sequence is:
[tex]f(k) = \frac{k^3}{k^4 + 10}[/tex]
Hence the limit is:
[tex]\lim_{k \rightarrow \infty} f(k) = \lim_{k \rightarrow \infty} \frac{k^3}{k^4 + 10} = \lim_{k \rightarrow \infty} \frac{k^3}{k^4} = \lim_{k \rightarrow \infty} \frac{1}{k} = \frac{1}{\infty} = 0[/tex]
Hence, the infinite sequence converges, as the limit does not go to infinity.
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The series diverges by the comparison test.
We have for large enough [tex]k[/tex],
[tex]\displaystyle \frac{k^3}{k^4+10} \approx \frac{k^3}{k^4} = \frac1k[/tex]
so that
[tex]\displaystyle \sum_{k=0}^\infty \frac{k^3}{k^4+10} = \frac1{10} + \sum_{k=1}^\infty \frac{k^3}{k^4+10} \approx \frac1{10} + \sum_{k=1}^\infty \frac1k[/tex]
and the latter sum is the divergent harmonic series.
Look at the equation shown below. 19 - 5 = 3 z - 11 Which of these expressions gives the value of Z
If the equation is 19-5=3z-11 then the value of z is 15/3.
Given an equation in terms of z is 19-5=3z-11.
We are required to find the value of variable z which exist in equation.
Equation is like a relationship between two or more variables expressed in equal to form. Equations of two or more variables look like ax+by=c. It may be linear equation, quadratic equation,cubic equation,or many more depending on power of the variable.
The value of z can be find as under:
19-5=3z-11
4=3z-11
3z=4+11
3z=15
z=15/3
Hence if the equation is 19-5=3z-11 then the value of variable z is 15/3.
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A blimp is 1600 meters high in the air and measures the angles of depression to two stadiums to the east of the blimp. if those measurements are 71.7° and 25.2°, how far apart are the two stadiums?
The two stadiums are 2,871 meters
A blimp = point A
stadium 1 = point B
stadium 2 = point C
height of the blimp , AD = 1600
depression angle of stadium 1 , ∠y = 71.7°
depression angle of stadium 2 , ∠x = 25.2°
distance between the two stadiums = d
So, it forms 2 triangles ABD and ACD,
Using the trigonometric ratios,
tan θ = Altitude / Base
DC = AD × tan (90° - x)
= 1600 × tan( 90° - 25.2° )
= 1600 × cot(25.2°)
= 1600 × 2.13
DB = AD × tan (90° - y)
= 1600 × tan( 90° - 71.7° )
= 1600 × cot(71.7°)
= 1600 × 0.33
∴ d = DC - DB
= 1600 * [ tan( 90° - 25.2° ) - tan( 90° - 71.7° ) ]
= 2,871 meters
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6. Solve the system of equations.
x = 3y + 1
2x+4y= 12
O (10,3)
O (4,1)
(1,4)
(3,10)
Answer:
(4, 1 )
Step-by-step explanation:
x = 3y + 1 → (1)
2x + 4y = 12 → (2)
substitute x = 3y + 1 into (2)
2(3y + 1) + 4y = 12
6y + 2 + 4y = 12
10y + 2 = 12 ( subtract 2 from both sides )
10y = 10 ( divide both sides by 10 )
y = 1
substitute y = 1 into (1)
x = 3(1) + 1 = 3 + 1 = 4
solution is (4, 1 )
i need help with this
The value of the x from the given equation is 1 and 6/7.
According to the statement
we have given that the quadratic equation and we have to find the solve for the value of the x.
So, For this purpose we know that the
A quadratic equation is any equation that can be rearranged in standard form as where x represents an unknown, and a, b, and c represent known numbers.
So, The given equation is
7x^2 -x -6 =0
Find the factors of the equation
7x^2 -7x + 6x -6 =0
7x(x-1) -6(x-1) = 0
(x-1)(7x-6) =0
here the values of x becomes 1 and 6/7.
So, The value of the x from the given equation is 1 and 6/7.
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RSM wants to send 4 of its 18 teachers into a conference. How many ways can they do this?
There are 18c4 ways that RSM wants to send 4 of its 18 teachers into a conference. that means there are 3060 ways to send
there are 18 teachers and RSM wants to send 4 mem out of 18
so, we use combinatorics for this
Combinatorics is the branch of Mathematics dealing with the study of finite or countable discrete structures. It includes the enumeration or counting of objects having certain properties. Counting helps us solve several types of problems such as counting the number of available IPv4 or IPv6 addresses.
It is used to find solutions easily for possible ways of a problem
For that we are using the formula for combinatorics
NCr = n!/ (r! (n – r)!)
similarly 18c4 = 18!/ (4! (18 – 4)!)
= 3060
Therefore , there are 3060 ways that RSM wants to send 4 of its 18 teachers into a conference.
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Isabelle is mixing red paint with blue paint to make purple paint. She adds 3/10 of a fluid ounce of red to 11/15 of a fluid ounce of blue to make 1 1/30fluid ounces of purple. How many fluid ounces of red paint will she need to make 3 fluid ounces of purple paint?
Answer:
27/31
Step-by-step explanation:
FIrst, construct a ratio. Isabelle needs 3/10 red to make 31/30 purple. So, we can divide red by purple to form a fraction to determine how much red paint for 1 fluid oz of purple. (3/10)/(31/30)=(9/30)/(31/30)=9/31. For every 1 oz of purple, we need 9/31 oz of red. Because we found how much red paint for 1 oz purple paint, we simply multiply by 3 to find how much red paint for 3 fluid oz of purple paint. (9/31)*3=27/31
3. What kind of triangle is represented by the triangle shown below?
Isosceles
Right
O Equilateral
Scalene
Answer:
Isosceles
Step-by-step explanation:
An Isosceles triangle has an acute angle (less than 45°), and this photo shows a triangle with two matching sides with one side being longer.
A right triangle would have a 90° angle which this photo doesn't have
An Equilateral triangle has all 60° sides, since it doesn't have all matching sides, it cannot be the answer.
A Scalene triangle is similar to this photo except it has 30° 60° and 90° angles, which this photo doesn't have.
I hope this helps!
Solve the right triangle. Round decimals to the nearest tenth
Answer: 42
Step-by-step explanation:
angle t is 42 degrees
Answer:
∠T = 42°
PT = 14.4
QT = 19.4
Step-by-step explanation:
An angle and its adjacent side are given in the right triangle. The other two sides can be found using trig relations. The third angle can be found using the angle sum theorem.
Trig relationsThe mnemonic SOH CAH TOA is intended to remind you of the relations between sides of a right triangle and the trig functions of its angles. The relations relevant to this triangle are ...
Cos = Adjacent/Hypotenuse ⇒ Hypotenuse = Adjacent/Cos
Tan = Opposite/Adjacent ⇒ Opposite = Adjacent×Tan
Then the missing side lengths are ...
QT = QP/cos(Q) = 13/cos(48°) ≈ 19.4282 ≈ 19.4
PT = PQ×tan(Q) = 13×tan(48°) ≈ 14.43796 ≈ 14.4
Angle sumThe angle sum theorem tells you the sum of angles in a triangle is 180°. This means the acute angles in a right triangle are complementary.
∠T = 90° -48° = 42°
The solution to the triangle is ...
∠T = 42°
PT = 14.4
QT = 19.4
__
Additional comment
The attachment shows the solution from one of many available triangle solvers. Some calculators have triangle solver functions built in.
For what value of x is 3 − x equal to x − 3?
Answer:
x = 3
Step-by-step explanation:
Given the information from the question, we can deduce that:
3 - x = x - 3
Now our goal here is to find x.
3 - x = x -3
3 - x - 3 = x - 3 - 3
- x = x - 6
- x - x = x - 6 - x
- 2x = - 6
x = [tex]\frac{-6}{-2}[/tex] = 3
Answer: 3
Step-by-step explanation: The only value for x in which 3 - x is the same as x - 3 is where x does not affect the value of 3 whatsoever. We can also set this up algebraically to find this out algebraically.
x - 3 = 3 - x
Adding 3 to both sides, we have
x = 6 - x
Adding x to both sides we have
2x = 6
Dividing by 2 from both sides, we get
x = 3
Everyone in Sandy's class has to do a science project. Out of 50 students, 56% have completed their projects.
How many students still need to do their projects?
Pls help ASAP
Answer:
22
Step-by-step explanation:
100 - 56 is 44. 44% have still not done the project
.44 x 50 = 22
Answer:
22 coz 56% of 50 which is the total is 28. Then the remaining 44%is22
Step-by-step explanation:
Look at the diagram below
Answer:
TRUE
Since , Angle ABD is congruent or equal to Angle CBD
we know that sides opposite to equal angles are also equal.
i.e AD and CD are opposite sides to angles ABD and CBD respectively.
So, AD = CD
PLSSS HELP ASAP!! ty
On a graph, sketch f(x)=x+3 and g(x)=x. Is there a way of determining the graph of f(x)+g(x) without solving it algebraically? Explain your thinking below.
The graph of f(x) = x + 3 and g(x) = x is sketched using the geogebra tool. The way of determining the graph of f(x) + g(x) is by adding the y-coordinate of g(x) to the y-coordinate of f(x).
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.
An exponential function is in the form:
y = abˣ
Where a is the initial value and b is the multiplication factor.
The graph of f(x) = x + 3 and g(x) = x is sketched using the geogebra tool. The way of determining the graph of f(x) + g(x) is by adding the y-coordinate of g(x) to the y-coordinate of f(x).
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What is the twentieth term in the sequence 23, 43, 63, 83 …?
Answer:
403 (hope this helps)
Step-by-step explanation:
The ball followed a path modelled by the equation h = −0.001! + 0.5 + 2.5 where h is the height of the ball in feet and is the horizontal distance in feet.
1) Represent the distance-height relationship for each player’s ball as an equation, in a table and on a graph. Record each representation and clearly label which player the information belongs to.
2) Supposed there were no obstacles.
a. Whose ball would travel the greatest distance before hitting the ground?
b. Whose ball would travel the shortest distance before hitting the ground?
3) Suppose the fence was 350 ft from home plate. At what height was each ball when it passed over the fence?
The heights the balls hit a fence at 350 ft distance are 65 feet, 38 feet and 30 feet, respectively
Represent the distance-height relationship for each player’s ball as an equation, in a table and on a graph.Juan
Juan's equation is given as:
h = -0.001d^2 + 0.5d + 2.5
h =
Set d to multiples of 50 from 0 to 400.
So, the table of values of Juan's function is:
d (ft) h(ft)
0 2.5
50 25
100 42.5
150 55
200 62.5
250 65
300 62.5
350 65
400 42.5
See attachment for the graph of Juan's function
Mark
A quadratic function is represented as:
h = ad^2 + bd + c
Using the values on the table of values, we have:
c = 3 -- the constant value
So, the equation becomes
h = ad^2 + bd + 3
Using the two other values on the table of values, we have:
23 = a(50)^2 + b(50) + 3
38 = a(100)^2 + b(100) + 3
Using a graphing tool, we have:
a = -0.001
b = 0.45
So, Mark's equation is h(d) = -0.001d^2 + 0.45d + 3
See attachment for Mark's graph.
Barry
From the graph, we have the table of values of Barry's function to be:
d (ft) h(ft)
0 2.5
50 21
100 35
150 44
200 48
250 46
300 41
350 30
400 14
450 0
Using a graphing tool, we have the quadratic function to be:
y = -0.001x^2 +0.4x +2.5
The shortest and the greatest distance before hitting the groundFrom the graphs, equations and tables, the distance travelled by the balls are:
Juan = 505 feet
Mark = 457 feet
Barry = 450 feet
This means that Juan's ball would travel the greatest distance while Barry's ball would travel the shortest.
The height the balls hit a fence at 350 ft distanceTo do this, we set d = 350
From the graphs, equations and tables, the height at 350 ft by the balls are:
Juan = 65 feet
Mark = 38 feet
Barry = 30 feet
The above represents the height the balls hit the fence
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Solve for x.
x/3 ≤ −6
x / 3 ≤ -6
---Multiply both sides by 3 to cancel out the denominator on the left side
x ≤ -18
Hope this helps!
Answer:
x=18 we multiply both 6and3Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
The range of the quadratic function y = (2 / 3) · x² - 6 is {- 6, 0, 18, 48}.
What is the range of a quadratic equation?
In this case we have a quadratic equation whose domain is stated. The domain of a function is the set of x-values associated to only an element of the range of the function, that is, the set of y-values of the function. We proceed to evaluate the function at each element of the domain and check if the results are in the choices available.
x = - 9
y = (2 / 3) · (- 9)² - 6
y = 48
x = - 6
y = (2 / 3) · (- 6)² - 6
y = 18
x = - 3
y = (2 / 3) · (- 3)² - 6
y = 0
x = 0
y = (2 / 3) · 0² - 6
y = - 6
x = 3
y = (2 / 3) · 3² - 6
y = 0
x = 6
y = (2 / 3) · 6² - 6
y = 18
x = 9
y = (2 / 3) · 9² - 6
y = 48
The range of the quadratic function y = (2 / 3) · x² - 6 is {- 6, 0, 18, 48}.
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Solve the following system using the algebraic method of substitution. Verify your solution.
x + 2y = -5
3x - y = -1
Solve the following linear system using the algebraic method of elimination. Verify your solution.
x + 2y = 2
3x + 5y = 4
Solve the following linear system algebraically. State why you chose the method you used.
x + 3y = 7
2x + 4y = 11
Answer: Look into step by step
Step-by-step explanation:
1. Multiply the second equation by 2; 6x - 2y = -2 then add to first equation
7x = -7 so x = -1, substitute x = -1 into the first equation -1 + 2y = -5 so y = -2
2. Multiply the first equation by 3; 3x + 6y = 6 then subtract it by second equation
y = 2, substitute y = 2 into first equation, x + 4 = 2, x = -2
3. Multiply the first equation by 2; 2x + 6y = 14 then subtract it by second equation
2y = 3 so y = 1.5, substitute y = 1.5 into the first equation x + 4.5 = 7, x = 2.5
I chose this method as it is easy