SOLUTION: (y+10)*X=1800 (x+10)*Y = 2000

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Question 102460: (y+10)*X=1800
(x+10)*Y = 2000
Answer by Fombitz(32388) About Me  (Show Source):
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1.(Y+10)*X=1800
2.(X+10)*Y = 2000
Use one equation to solve for one variable in terms of another and then solve using the second equation. Let's use equation 2 and solve for Y.
%28X%2B10%29%2AY+=+2000
cross%28X%2B10%29%2AY%2Fcross%28X%2B10%29=2000%2F%28X%2B10%29
Y=2000%2F%28X%2B10%29
Now use equation (1) and substitute for Y
%28Y%2B10%29%2AX+=+1800
%282000%2F%28X%2B10%29%2B10%29%2AX+=+1800 Substitute
2000%2AX%2F%28X%2B10%29%2B10%2AX+=+1800Distributive property
%282000%2B10%2A%28X%2B10%29%29%2AX+=+1800%2A%28X%2B10%29 Multiply both sides by (X+10)
2000%2AX%2B10%2A%28X%5E2%29%2B100%2AX+=+1800%2AX%2B18000Distribute and simplify.
10%2A%28X%5E2%29%2B300%2AX-18000+=+0Additive inverse of 1800x and 20000.
X%5E2%2B30%2AX+-1800+=+0Divide by 10.
%28X%2B60%29%2A%28X-30%29+=+0Factor the equation.
X=-60 and X=30
From equation (2),
2.%28X%2B10%29%2AY+=+2000
For X=-60,
%28-60%2B10%29%2AY+=+2000
%28-50%29%2AY+=+2000
Y=-40
For X=30,
%28Y%2B10%29%2AY+=+2000
%2830%2B10%29%2AY+=+2000
%2840%29%2AY+=+2000
Y=50
Two solution pairs:
X=-60 and Y=-40
and
X=30 and Y=50