Question

Solve the system of linear equations using substitution. The system is x=2y + 7 and 3x-2y=3

Answer 1

First, solve for either x or y. Since the first is already solved for x, solve the second for x as well;
$x=2y+7\\3x-2y=3\\\\ 3x-2y=3\\3x=2y+3\\x=\frac{2}{3}y+1\\\\ Since~x=x,~substitute~equations~in:\\x=x\\2y+7=\frac{2}{3}y+1\\1\frac{1}{3}y=-6\\y=\frac{-6}{\frac{4}{3}}=-6*\frac{3}{4}\\y=\frac{-9}{2}=-4.5\\\\ Plug~-4.5~in~for~y:\\x=2y+7\\x=2(-4.5)+7\\x=-9+7=-2\\\\ x=-2\\y=-4.5$