Question

Please help me with this question I am trying to help my son to understand this problem. Solve the system of equations using the substitution method. {y=−3x+7 x=−2y−16} Enter your answers in the boxes. x=____ y=___

Answer 1

We have the next system of equations:

$\begin{gathered} y=-3x+7\text{ (eq. 1)} \\ x=-2y-16\text{ (eq. 2)} \end{gathered}$

Substituting equation 1 into equation 2 and solving for x:

$\begin{gathered} x=-2(-3x+7)-16 \\ x=-2(-3x)+(-2)\cdot7-16\text{ (Distributing}) \\ x=6x-14-16 \\ x=6x-30 \\ x-6x=6x-30-6x \\ -5x=-30 \\ \frac{-5x}{-5}=\frac{-30}{-5} \\ x=6 \end{gathered}$

Substituting x = 6 into equation 1:

$\begin{gathered} y=-3\cdot6+7 \\ y=-18+7 \\ y=-11 \end{gathered}$