Statement best describe the system of equations for y = 3x + 7 x = -3x - x the equations have different slopes in different y intercepts does the system has one solution at negative 3, 7 both equations have a slope of negative 3 but they do not share the same y intercept that's the system has no solution because the lines are pretty well

Answer 1

Let's analyze the given equations step by step.

1. You have the first equation: \[ y = 3x + 7 \] Here, the slope is 3 and the y-intercept is 7.

2. For the second equation: \[ x = -3x - x \] This is equivalent to simplifying it: \[ x = -4x \] Adding \(4x\) to both sides gives: \[ 5x = 0 \implies x = 0 \] This represents a vertical line where \(x = 0\).

Since the equations represent different types of lines (one is a linear function with a positive slope and the other is a vertical line), let's summarize our findings:

• The first equation has a slope of 3 and a y-intercept of 7, meaning it rises steeply as \(x\) increases.
• The second equation \(x = 0\) is a vertical line along the y-axis.

Conclusion about the system:

1. Different slopes: The slope of the first line is 3, while the second line does not have a slope (as vertical lines are undefined). Therefore, they do not have the same slope.

2. Different y-intercepts: The first equation intersects the y-axis at 7, while the second does not intersect the y-axis at all since it is a vertical line.

3. One solution: Since the first equation is a sloped line and the second is a vertical line, they will intersect at exactly one point. If you plug \(x = 0\) into the first equation to find \(y\): \[ y = 3(0) + 7 = 7 \] So the point of intersection is (0, 7), not (-3, 7).

4. No solution: It is incorrect to say there is no solution because the two lines do intersect at one unique point.

So, the correct statement about the system of equations is that it has one solution at the point (0, 7), with the lines having different slopes and y-intercepts.