Chapter 5.1, Problem 14E

To determine

To solve: the system of linear equation.

Answer to Problem 14E

All of the equalities are true; the ordered pair $\left(4,0\right)$ is the solution of the system.

Explanation of Solution

Given:

  $\begin{array}{l}y=-x+4\\ y=2x-8\end{array}$

Calculation:

  $\begin{array}{l}y=-x+4\\ y=2x-8\end{array}$

Since both expressions $-x+4$ and $2x-8$ are equal to y

Set them equal to each other forming an equation in x

  $-x+4=2x-8$

Move variable x to the left side and change its sign

  $\begin{array}{l}-x-2x+4=-8\\ -x-2x=-8-4\end{array}$

Collect like terms

  $-3x=-12$

Divide both sides by -2

  $\begin{array}{l}\frac{-3x}{-3}=\frac{-12}{-3}\\ x=4\end{array}$

Substitute the value of x into the equation

  $\begin{array}{l}y=-x+4\\ y=-4+4\end{array}$

Solve the equation for y

  $y=0$

The possible solution of the system is the ordered pair $\left(x,y\right)=\left(4,0\right)$

Check if the given ordered pair is the solution of the system of equations

  $\begin{array}{l}0=-4+4\\ 0=2\times 4-8\end{array}$

Simplify the equalities

  $\begin{array}{l}0=0\\ 0=0\end{array}$

Since all of the equalities are true, the ordered pair $\left(4,0\right)$ is the solution of the system.

  

Conclusion:

Therefore, all of the equalities are true; the ordered pair $\left(4,0\right)$ is the solution of the system.