# For what values of m and n is (5,-3) the solution of the equations:mx-y=23 nx+y=12

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We have to find the values of m and n for which the solution of x and y is (5,-3). To do this we substitute x= 5 and y=-3 in the equations and solve for m and n.

mx-y=23

=> 5m + 3 = 23

=> 5m = 23 - 3

=> 5m = 20

=> m = 20/ 5

=> m = 4

nx+y=12

=> 5n - 3 = 12

=> 5n = 12+3

=> 5n = 15

=> n = 15/5

=> n = 3

**The required values of m and n are 4 and 3 respectively**

From the 1st equation,

mx-y=23

m(5) - (-3) = 23

5m + 3 = 23

5m = 23 - 3 = 20

m = 20 / 5 = 4

From 2nd equation,

nx+y=12

n(5) + (-3) = 12

5n = 15

n = 15 / 5 = 3

Therefore, the required answers are: **m=4 and n=5**

The given lines are :

mx-y = 23...(1)

nx+y = 12...(2)

The point of intersection (or solution for x and y) = (5,-3) is given.

Adding the equations, we get:

(m+n)x = 23+12 = 35, so x= 35/(m+n)

(2)-(1) gives: 2y = 12-23 = -11, so y = -9/2= -4.5.

So 35/(m+n) = 5, Or m+n = 5/35 = 1/7.

y = -4.5 cannot be -3.

Therefore for no values of m and n the two equations, can have the solution (5, -3).