Question

In the equation

ax + cy = n
-bx + ry = n

Solve by the following process

If you eliminate x what will we have to multiply both equations by!

Answer 1

first one by b, second one by a

Answer 2

get
\[abx+bcy=bn\]
\[-abx+ary=an\]

Answer 3

add and the x's will drop out
\[(bc+ar)y=(a+b)n\]

Answer 4

\[y=\frac{(a+b)n}{bc+ar}\]

Answer 5

Could you show step by step?

Answer 6

well actually those are the steps. you want the x's to drop out. the first equation shows ax and the second shows -bx
you want the coefficients to work out so that one is the negative of the other

Answer 7

if you multiply the first one by b you bet abx and if you multiply the second one by a you get -abx and now one is the negative of the other

Answer 8

for example if one had 5x and the other had -3x you would multiply the top one by 3 and the bottom one by 5 to get 15x and -15x
then they would "cancel' (add up to zero) when you added the equations

Answer 9

ax + cy = n
-bx + ry = n
multiply first by B and second by a?