Question 1003807
for what values of m and n is (5,-3) the solution for (x,y)?

The equations being: 
<pre>
{{{system(mx-y=23,nx+y=12)}}}

We substitute (5,-3) for (x,y) in both equations:

{{{system(m(5)-(-3)=23,n(5)+(-3)=12)}}}

Simplify them:

{{{system(5m+3=23,5n-3=12)}}}

Simplify further:

{{{system(5m=20,5n=15)}}}

And finally:

{{{system(m=4,n=3)}}}

---------------

Checking

{{{system(mx-y=23,nx+y=12)}}}

becomes:

{{{system(4x-y=23,3x+y=12)}}}

Adding the two equations to eliminate y

{{{7x=35}}}
{{{x=5}}}

Substituting 5 for x in 4x-y=23:

   4x-y=23
4(5)-y = 23
  20-y = 23
    -y = 3
     y = -3

(x,y) = (5,-3)

So it's correct.

Edwin</pre>