Question

Solve 3x+2y=7 and x-4y=-21 by using substitution

Answer 1

$3x+2y=7 \\ x-4y=-21 \\ \\ \hbox{solve the second equation for x:} \\ x-4y=-21 \\ x=4y-21 \\ \\ \hbox{substitute 4y-21 for x in the first equation:} \\ 3(4y-21)+2y=7 \\ 12y-63+2y=7 \\ 14y=7+63 \\ 14y=70 \\ y=\frac{70}{14} \\ y=5 \\ \\ x=4y-21=4 \times 5-21=20-21=-1 \\ \\ \boxed{(x,y)=(-1,5)}$