Exercise 15 Page 268

We are given a system of equations. y=-3x+6 & (I) y=3x-12 & (II) We are asked which of the given statements that describe the system are true. &The graph of the system is a pair of &lines that do not intersect. &The graph of the system is a pair of &lines that do not intersect. &The graph of the system is a pair of &lines that intersect in every point. &The system has no solution. &The system has1solution. &The system has infinitely &many solutions. To determine if the first three statements are true, we need to graph the system. To do that, we will first identify the slopes and the initial values. Since both equations are in slope-intercept form, this is not a problem.

Equation	Slope	Initial Value
y= -3x+ 6	-3	6
y= 3x -12	3	-12

To graph these equations, we will start by plotting their initial values. Then, we will use the slope to determine another point that satisfies each equation, and connect the points with a line.

We can see that the lines intersect at exactly one point.

Now, we know that the first and third given statements are false and that the second statement is true. *&The graph of the system is a pair of &lines that do not intersect. ✓&The graph of the system is a pair of &lines that intersect at exactly one point. *&The graph of the system is a pair of &lines that intersect in every point. Since there is only one point of intersection of the lines, the system of equations has only one solution. Thus, the fourth and sixth statements are false and the fifth statement is true. *&The graph of the system is a pair of &lines that do not intersect. ✓&The graph of the system is a pair of &lines that intersect at exactly one point. *&The graph of the system is a pair of &lines that intersect in every point. *&The system has no solution. ✓&The system has1solution. *&The system has infinitely &many solutions.