Question 102460
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. 
{{{(X+10)*Y = 2000}}}
{{{cross(X+10)*Y/cross(X+10)=2000/(X+10)}}}
{{{Y=2000/(X+10)}}}
Now use equation (1) and substitute for Y

{{{(Y+10)*X = 1800}}}
{{{(2000/(X+10)+10)*X = 1800}}} Substitute
{{{2000*X/(X+10)+10*X = 1800}}}Distributive property
{{{(2000+10*(X+10))*X = 1800*(X+10)}}} Multiply both sides by (X+10)
{{{2000*X+10*(X^2)+100*X = 1800*X+18000}}}Distribute and simplify.
{{{10*(X^2)+300*X-18000 = 0}}}Additive inverse of 1800x and 20000.
{{{X^2+30*X -1800 = 0}}}Divide by 10.
{{{(X+60)*(X-30) = 0}}}Factor the equation. 
{{{X=-60}}} and {{{X=30}}}
From equation (2),
{{{2.(X+10)*Y = 2000}}}
For X=-60,
{{{(-60+10)*Y = 2000}}}
{{{(-50)*Y = 2000}}}
{{{Y=-40}}}
For X=30,
{{{(Y+10)*Y = 2000}}}
{{{(30+10)*Y = 2000}}}
{{{(40)*Y = 2000}}}
{{{Y=50}}}
Two solution pairs:
X=-60 and Y=-40
and
X=30 and Y=50