solve by linear combination

Question

3x+7y=-2

2x+3y=-3

Answer 1

If you multiply the 1st equation by 2 and the 2nd equation by (-3) you will get 

 

 6x + 14y = -4

-6x -   9y =   9

 

If you add these 2 equation together you will get

 

0x + 5y = 5

y = 1

 

If you plug this value in to the original 1st equation you will get 

 

3x + 7(1) = -2

3x + 7 = -2

3x = -9

x = -3

 

So x = -3 and y = 1

 

Check:  3(-3) + 7(1) = -9 + 7 = -2

            2(-3) + 3(1) = -6 + 3 = -3