A coordinate plane with 4 quadrants ranges from negative 10 to 10 in unit increments on both the x and y axes. A solid line and a dashed line with arrows at both the ends are drawn parallel to each other on the graph. The equation of the solid line is y equals 3 x minus 2. The equation of the dashed line is negative 3 x plus y equals 7.

Question

The graphs represent this system:  

y=3x−2


−3x+y=7
 

How many solutions does this system have: 0, 1, or ∞
?

(1 point)

Answer 1

To determine how many solutions the system of equations has, we need to analyze the lines given:

1. The equation of the solid line is \(y = 3x - 2\).

2. The equation of the dashed line can be rewritten in slope-intercept form (i.e., \(y = mx + b\)). We can rearrange the equation \(-3x + y = 7\) to:

   \[y = 3x + 7\]

Now we can compare the two lines:

• The solid line has a slope of 3 and a y-intercept of -2.
• The dashed line also has a slope of 3 but a different y-intercept of 7.

Since the slopes of both lines are the same (both are 3), the lines are parallel. Because they have different y-intercepts, they never intersect.

Since parallel lines do not intersect, this system of equations has 0 solutions.