Solve for x and y using elimination

ax+by=c
bx+ay=c

This question has been confusing me for a long time, and I can't seem to find the answer by solving using elimination.
Thanks for helping me :)

1 answer

multiply #1 by b and #2 by a, and you have

abx+b^2y = bc
abx+a^2y = ac

now subtract

(b^2-a^2)y = (b-a)c
y = c/(a+b)

and use that to find x. Or, start all over and multiply by a and b to remove the y terms.