Q. 69 - Intermediate Algebra

Question

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

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

Step-by-Step Solution

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 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:$\begin{array}{r}3x+y=12\end{array}$

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:$(1,9)$