Question

Consider the equations and graph below.

y = negative 3 (x minus 1). Y = negative 3 x minus 1

On a coordinate plane, 2 lines are parallel to each other.

Which explains why this system has no solution?
Each has a slope of –3 and a y-intercept of –1, which makes the lines parallel.
Each has a slope of –3 and a y-intercept of –1, which makes the lines equivalent.
Each has a slope of –3, but one has a y-intercept of 3 and the other has a y-intercept of –1, which makes the lines parallel.
Each has a slope of –3, but one has a y-intercept of 3 and the other has a y-intercept of –1, which makes the lines equivalent.

Answer 1

To explain why the system of equations has no solution, we need to analyze the equations:

1. **First Equation:** \( y = -3(x - 1) \)
- This can be rewritten in slope-intercept form:
- \( y = -3x + 3 \)
- The slope is \(-3\) and the y-intercept is \(3\).

2. **Second Equation:** \( y = -3x - 1 \)
- The slope is \(-3\) and the y-intercept is \(-1\).

Now, let's consider the characteristics of these two lines:
- Both lines have the same slope of \(-3\), which means they are parallel to each other.
- The y-intercept of the first line is \(3\) and of the second line is \(-1\), so they do not intersect.

Thus, the correct explanation for why this system has no solution is:

**Each has a slope of –3, but one has a y-intercept of 3 and the other has a y-intercept of –1, which makes the lines parallel.**