How to solve a bilinear equation?

Question

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How to solve:
7x+42y=32
32x+17y=-6?

Answer 1

To eliminate x multiply the first equation by 32 and the second by 7:

224x+1344y=1024

224x+119y=-42

Subtract the 2nd from the 1st:

1225y=1066, so y=1066/1225.

Now go back to the original equations and substitute for y in either: 7x=32-42*1066/1225=-796/175, making x=-796/1225. CHECK: Substitute for x and y in both equations:

-796/175+6396/175=5600/175=32

-25472/1225+18122/1225=-7350/1225=-6.