SOLUTION: for what values of m and n is (5,-3) the solution for (x,y)? The equations being: mx-y=23 nx+y=12 Can you please explain this question?

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: for what values of m and n is (5,-3) the solution for (x,y)? The equations being: mx-y=23 nx+y=12 Can you please explain this question?       Log On


   

Question 1003807: for what values of m and n is (5,-3) the solution for (x,y)?
The equations being:
mx-y=23
nx+y=12
Can you please explain this question?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
for what values of m and n is (5,-3) the solution for (x,y)?
The equations being: 
system%28mx-y=23%2Cnx%2By=12%29

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

system%28m%285%29-%28-3%29=23%2Cn%285%29%2B%28-3%29=12%29

Simplify them:

system%285m%2B3=23%2C5n-3=12%29

Simplify further:

system%285m=20%2C5n=15%29

And finally:

system%28m=4%2Cn=3%29

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

Checking

system%28mx-y=23%2Cnx%2By=12%29

becomes:

system%284x-y=23%2C3x%2By=12%29

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