Solve this simultaneous equation using substitution method
2m - n = 5 ..............(1)
3m + 2n = -24 .............(2)
From equation (1), we can rearrange it to solve for m:
2m = n + 5
m = (n + 5)/2
Now substitute this expression for m into equation (2):
3((n + 5)/2) + 2n = -24
Multiply through by 2 to eliminate the fraction:
3(n + 5) + 4n = -48
Distribute the 3:
3n + 15 + 4n = -48
Combine like terms:
7n + 15 = -48
Subtract 15 from both sides:
7n = -63
Divide by 7:
n = -63/7
n = -9
Now substitute this value of n back into equation (1) to solve for m:
2m - (-9) = 5
2m + 9 = 5
Subtract 9 from both sides:
2m = -4
Divide by 2:
m = -4/2
m = -2
So the solution to the simultaneous equations is m = -2 and n = -9.