Question

Solve the system of equations $3x+y=12,x=y-8$by substitution and explain all your steps in words.

Short answer

The ordered pair is$(1,9)$

Step-by-step solution

Step 1. Given Information

The given set of equations are

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

Step 2. Calculation

Solve the given set of equations by using substitution method.

Substitute the value of x from second equation in equation first to find the value of y.

$$\begin{gathered} 3x+y=12 \\ 3(y-8)+y=12 \\ 3y-24+y=12 \\ 4y=36 \\ y=9 \end{gathered}$$

Substitute the value of y in equation second and solve for x.

$$\begin{gathered} 3x+y=12 \\ 3x+9=12 \\ 3x=3 \\ x=1 \end{gathered}$$

Thus, the ordered pair is$(1,9)$