Chapter 8.10, Problem 1CYU

To determine

The solution of the $y=-x$ and $y=x-4$ by using the graphing method

Answer to Problem 1CYU

The solution of $y=-x$ and $y=x-4$ is $x=-4,y=4$

Explanation of Solution

Given:

The two eqn are as:

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

Calculation:

The two eqns. are described as:

  $y=-x$..........(1)

  $y=x-4$..........(2)

Now, need to draw the graph of the first equation which is already in $y$ - intercept form. So, check the following graph for the first eq. $y=-x$

  

Now, need to draw a graph for the second equation $y=x-4$

  

From graph of two equations; understands that these two lines intersects at the point $\left(-4,4\right)$

So, the point of intersection $\left(-4,4\right)$ is the solution of equation sets $\begin{array}{l}y=-x\\ y=x-4\end{array}$

The solution is $x=-4,y=4$

Conclusion:

Hence, there is one solution for the given equation set which is its point of intersection.