Chapter 5.5, Problem 36E

To determine

Whether solution of a system of equation is the intersecting point of the two lines of the system.

Answer to Problem 36E

Solution of the system of equation is $\left(4,0\right)$ .

Explanation of Solution

Given information:

The graphs of $y=-x+4$ and $y=2x-8$ intersect at the point $\left(4,0\right)$ . So the solution of the equation $-x+4=2x-8$ is $\left(4,0\right)$ .

Calculation:

Equation:

  $-x+4=2x-8$

Write a system of linear equation using each side of the original equation

  $\begin{array}{l}y=-x+4\text{Equation}1\\ y=2x-8\text{Equation}2\end{array}$

As the graphs of the equation $-x+4=2x-8$ intersects at $\left(4,0\right)$ .

And the equation is only in one variable. Solution of the equation is $x=4$ , where the corresponding value of $y=0$ .

Hence your friend is wrong saying $\left(4,0\right)$ is the solution of the given equation.

Check:

Substitute $x=4$ , in given equation.

  $\begin{array}{c}-x+4=2x-8\\ -4+4=2\cdot 4-8\\ 0=0\end{array}$

Which is true hence solution of the given equation is $\left(4,0\right)$ .