Question

All of the statements are TRUE, except:

A. Systems whose equations have different slopes have one solution.
B. Systems whose equations have the same slope and the same y-intercept have infinitely many solutions.
C. Systems whose equations have the same slope and the same y-intercept have one solution.
D. Systems whose equations have the same slope and different y-intercepts have no solution.

Answer 1

The statement that is NOT true is option C. Systems whose equations have the same slope and the same y-intercept have infinitely many solutions, not just one.

Step-by-step explanation:

The statement that is NOT true is option C. Systems whose equations have the same slope and the same y-intercept have infinitely many solutions, not just one. This is because when the two equations have the same slope and the same y-intercept, they are overlapping lines and every point on one line is also on the other line.

For example, let's consider the equations y = 2x + 3 and y = 2x + 3. Both equations have the same slope (2) and the same y-intercept (3). If we graph these equations, we will see that the lines are identical and there are infinite points of intersection.

In contrast, when the equations have different slopes (option A) or the same slope but different y-intercepts (option D), there will be either one solution or no solution.