Chapter 6.6, Problem 104PPSE

Solution

To graph and solve: The system of equations $\left\{\begin{array}{l}y=x-6\hfill \\ y=x+6\hfill \end{array}\right.$ .

  

The system of equations has no solution.

Given information:

The system of equations, $\left\{\begin{array}{l}y=x-6\hfill \\ y=x+6\hfill \end{array}\right.$ .

Calculation:

Find two points on the line $y=x-6$ as follows.

When $x=0$ , $y=0-6=-6$ .

When $x=2$ , $y=2-6=-4$ .

Therefore, two points are $\left(0,-6\right)$ and $\left(2,-4\right)$ .

Now, find two points on the line $y=x+6$ .

When $x=2$ , $y=2+6=8$ .

When $x=0$ , $y=0+6=6$ .

So, two points are on the line $y=x+6$ are $\left(0,6\right)$ and $\left(2,8\right)$ .

Now, draw the lines on the same coordinate axes using the points.

  

Observe that the lines are parallel. This means that these lines do intersect each other. So, the there is no solution to the system of equations.

Conclusion:

The system of equations has no solution.