Question

Part 1: Explain, in complete sentences, how you would use the elimination method to solve the following system of equations. (3 points)

Part 2: Provide the solution to the system. (1 point)

2x + 9y = 4
3x + 7y = –7

Part 1: Explain, in complete sentences, how you would use the substitution method to solve the following system of equations. (3 points)

Part 2: Provide the solution to the system. (1 point)

5x – y = –2
10x – 3y = –7

Answer 1

I would multiply the 1st equation by -3 and the 2nd equation by 2. By doing this, the x's will cancel out (thus the elimination method).

2x + 9y = 4 -->(-3)
3x + 7y = -7 -->(2)
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-6x - 27y = -12 (result of multiplying by -3)
6x + 14y = -14 (result of multiplying by 2)
------------------add
0 - 13y = - 26
-13y = -26
y = -26/-13 (negative divided by negative equals positive)
y = 2
Now sub 2 in for y in either of the original equations
2x + 9y = 4
2x + 9(2) = 4
2x + 18 = 4
2x = -18 + 4
2x = - 14
x = -14/2
x = -7
you can now check your answers
3x + 7y = -7 2x + 9y = 4
3(-7) + 7(2) = -7 2(-7) + 9(2) = 4
-21 + 14 = -7 -14 + 18 = 4
-7 = -7 (correct) 4 = 4 (correct)
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You want to pick an equation and isolate a variable in it. Then sub what that variable equals into the other equation and solve for the other variable.

5x - y = -2
-y = -2 - 5x (multiply by -1 to make y positive)
y = 5x + 2

now sub 5x + 2 in for y in the other equation
10x - 3y = -7
10x - 3(5x + 2) = -7
10x - 15x - 6 = -7
-5x - 6 = -7
-5x = -7 + 6
-5x = -1
x = -1/-5
x = 1/5

now sub 1/5 in for x in the 1st equation
5x - y = -2
5(1/5) - y = -2
1 - y = -2
-y = -2-1
-y = -3 (multiply by -1 to make y positive)
y = 3

now check your answers
5x - y = -2 10x - 3y = -7
5(1/5) - 3 = -2 10(1/5) - 3(3) = -7
1 - 3 = -2 2 - 9 = -7
-2 = -2 (correct) -7 = -7 (correct)