Question

How to solve through elimination the following 2m=-4n-4 and 3m+5n=-3

Answer 1

$2m=-4n-4 \ \ \ |\times (-3) \\ 3m+5n=-3 \ \ \ |\times 2 \\ \\ -6m=12n+12 \\ \underline{6m+10n=-6} \ \ \ |\hbox{add the sides of the equations} \\ 10n=12n+12-6 \\ 10n=12n+6 \ \ \ |-12n \\ -2n=6 \ \ \ |\div (-2) \\ n=-3 \\ \\ 2m=-4n-4 \\ 2m=-4 \times (-3)-4 \\ 2m=12-4 \\ 2m=8 \ \ \ |\div 2 \\ m=4 \\ \\ (m,n)=(4,-3)$