Solve using the elimination method

Solve
7x + 4y = 17
3x - 2y = -15
using the elimination method.

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To use the elimination method, you need to get the coefficients of one of the variables to be the same, only with one being positive and one being negative, preferably.

7x + 4y = 17
3x - 2y = -15

7x + 4y = 17 {top equation stays the same}
6x - 4y = -30 {multiplied bottom equation by 2}
———————-
13x = -13 {added the two equations together}
x = -1 {divided each side by 13}

To solve for y, substitute -1, in for x, into one of the two equations.

7x + 4y = 17 {top equation}
7(-1) + 4y = 17 {substituted -1, in for x, into top equation}
-7 + 4y = 17 {multiplied 7 by -1}
4y = 24 {added 7 to each side}
y = 6 {divided each side by 4}

x = -1 and y = 6
(-1,6) is the point of intersection of the two lines

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