For each linear system, what values of m and n will produce the solution (5, -3)?

Question

mx +ny = -11 3mx + 4ny = 30
2mx - 3ny = 8 2mx - 5ny = 20

Answer 1

Assuming each system is on one line,

mx + ny = -11
3mx + 4ny =30

Plugging in 5 for x and -3 for y gives
5m - 3n = -11 ==> 15m - 9n = -33
15m -12n = 30

Subtract the second equation from the first:
(15m -15m) + (-9n - (-12n)) = (-33 - (30))
3n = -63 n = -21

5m - (3)(-21) = -11
5m + 63 = -11
5m = -74
m = -74/5

The second row would be done the same way.
If your systems are the vertical equation pairs instead of the horizontal pairs, same process applies. Good luck!

Answer 2

For 2mx - 3ny = 8 and 2mx - 5 ny = 20, subtract the second from the first and get 2ny = -12, so y = -6/n. Using this in the first, find x = -5/m. Thus (5,-3) = (-5/m,-6/n) when m = -1 and n = 2.

The procedure is the same for the other system: solve (by any method) for x and y. The solution will be in terms of m and n, then set the solution equal to (5,-3) and solve for m and n.