Question

Solve the system of equations by substitution and explain all your steps in words:

$\left\{\begin{array}{l}3x+y=12\\ x=y-8\end{array}\right.$

Short answer

The solution of system of linear equation$\left\{\begin{array}{l}3x+y=12\\ x=y-8\end{array}\right.$ is$(1,9)$

Step-by-step solution

Step 1. Given information and Solving equation

Given system of linear equations:

$\left\{\begin{array}{l}3x+y=12\\ x=y-8\end{array}\right.$

Firstly we will solve one equation for one valuable.

Consider equation $2$

Substitute $x=y-8$in equation

$3x+y=12$and solve for$y.$

Consider:localid="1644340563247" $\begin{array}{r}3x+y=12\end{array}$

Substitute and simplify parenthesis:

$\begin{array}{r}3(y-8)+y=12\\ 3y-24+y=12\end{array}$

$4y=36$

$y=36÷4$

$y=9$

Step 2. Solving for x

Now let us substitute $y=9$into

$x=y-8$and solve for$x$

On substituting we get:

$$\begin{gathered} x=9-8 \\ x=1 \end{gathered}$$

So the solution is:$(1,9)$