Question

Solve the system of equations by substitution.

$$\begin{gathered} 3x+y=12 \\ x=y-8 \end{gathered}$$

Short answer

The solution of the linear equation is that (1,9).

Step-by-step solution

Step 1. Given information

The given linear equations are:$$\begin{gathered} 3x+y=12 \\ x=y-8 \end{gathered}$$

Step 2.  Calculation

$$\begin{gathered} \mathrm{First}\mathrm{solve}\mathrm{one}\mathrm{equation}\mathrm{for}\mathrm{one}\mathrm{variable}. \\ \mathrm{Substitute}x=y-8\mathrm{in}\mathrm{equation}3x+y=12\mathrm{and}\mathrm{solve}fory. \\ 3x+y=12 \\ 3(y-8)+y=12 \\ 3y-24+y=12 \\ 4y=12+24 \\ 4y=36 \\ y=36/4 \\ =9 \end{gathered}$$

$$\begin{gathered} \mathrm{Substitute}y=9\mathrm{into} \\ x=y-8\mathrm{and}\mathrm{solve}\mathrm{for}x. \\ x=y-8 \\ x=9-8 \\ =1 \end{gathered}$$

localid="1644427920855" $$\begin{gathered} \mathbf{Check}\mathbf{:} \\ \mathrm{First}\mathrm{substitute}x=1,y=9 \\ \mathrm{into}\mathrm{the}\mathrm{equation}3x+y=12 \\ 3x+y=12 \\ 3\left(1\right)+9=12 \\ 3+9=12 \\ 12=12 \\ \mathrm{This}\mathrm{is}\mathrm{true}. \\ \mathrm{Also}\mathrm{substitute}x=1,y=9\mathrm{into}\mathrm{the}\mathrm{equation} \\ x=y-8 \\ x=y-8 \\ 1=9-8 \\ 1=1 \\ \mathrm{This}\mathrm{is}\mathrm{true}.\mathrm{Therefore},\mathrm{the}\mathrm{solution}\mathrm{of}\mathrm{the}\mathrm{system}\mathrm{of}\mathrm{linear}\mathrm{equations}\mathrm{is}\mathrm{that}(1,9) \end{gathered}$$