Chapter 8.8, Problem 4C

To determine

If the graphs of the two linear equations have different slopes, how many solutions does the related system have? Give a verbal and a graphical justification for your answer.

Answer to Problem 4C

There will be onesolution, if the graphs of the two linear equations have different slopes.

Explanation of Solution

We know that if the graphs of two linear equations have different slopes, then they will intersect exactly in one place.

We also know that the solution of a system of equation is the point, where the graphs of both equations intersect.

Let us assume that our system of equations is $y=-2x-12\text{and }y=x-3$ .

Let us graph our given system of equations. We can see that both equations are in slope-intercept form.

Upon graphing both equations, we will get our required graph as shown below:

  

Upon looking at our graph, we can see that both lines intersect at point $(-3,-6)$ . Therefore, there will be exactly one solution for a system of equations with different slopes.