The solution to the system of equations, 3m + 4n = 46 and 4m - 2n = -12, is: D. m = 2, n = 10.
How to solve a system of equations?
Given system of equations:
Equation 1: 3m + 4n = 46
Equation 2: 4m - 2n = -12
Multiply Equation 2 by 2 to make the coefficients of n in both equations cancel each other out when added:
Equation 1: 3m + 4n = 46
Equation 2 (multiplied by 2): 8m - 4n = -24
Now, add the two equations:
(3m + 4n) + (8m - 4n) = 46 - 24
11m = 22
m = 2
Now that we have the value for m, substitute it back into either Equation 1 or Equation 2. Let's use Equation 1:
3(2) + 4n = 46
6 + 4n = 46
Subtract 6 from both sides:
4n = 40
Divide by 4:
n = 10
So, the solution to the system of equations is option D. m = 2, n = 10.