Question

Solve the system of equations

Answer 1

$x-4y=5 \ \ \ |\hbox{multiply both sides by (-1)} \\ x-3y=2 \\ \\ -x+4y=-5 \\ \underline{x-3y=2 \ \ \ \ \ \ } \ \ \ |\hbox{add the sides of the equation} \\ -x+4y+x-3y=-5+2 \\ 4y-3y=-5+2 \\ y=-3 \\ \\ \hbox{replace y with -3 in one of the equations and solve for x:} \\ x-4y=5 \\ x-4 \times (-3)=5 \\ x+12=5 \\ x=5-12 \\ x=-7 \\ \\ (x,y)=(-7,-3)$