Question

Solve the system by substitution.

$$\begin{gathered} x+y=6 \\ y=3x-2 \end{gathered}$$

Short answer

The solution set is $(2,4)$.

Step-by-step solution

Step 1. Given Information 

We have to solve the system by substitution.

$$\begin{gathered} x+y=6 \\ y=3x-2 \end{gathered}$$

Step 2. Putting the value of y from the second equation in the equation x+y=6.

$$\begin{gathered} x+3x-2=6 \\ 4x-2=6 \\ \mathrm{Add}2\mathrm{on}\mathrm{both}\mathrm{side} \\ 4x-2+2=6+2 \\ 4x=8 \\ \mathrm{Divide}\mathrm{by}4\mathrm{on}\mathrm{both}\mathrm{side} \\ \frac{4}{4}x=\frac{8}{4} \\ x=2 \end{gathered}$$

Step 3. Putting the value of x in the equation y=3x−2

$$\begin{gathered} y=3\times 2-2 \\ y=6-2 \\ y=4 \end{gathered}$$