Use the image to answer the question.

Question

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.

The graphs represent this system:  

y=3x−2


−3x+y=7
 

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

Answer 1

To determine how many solutions the system has, we need to analyze the given equations.

1. The equation of the solid line is given as: \[ y = 3x - 2 \]

2. The equation of the dashed line can be rewritten from its original form: \[ -3x + y = 7 \implies y = 3x + 7 \]

Next, we evaluate the slopes and intercepts of these lines:

• The slope of the solid line \( y = 3x - 2 \) is \( 3 \).
• The slope of the dashed line \( y = 3x + 7 \) is also \( 3 \).

Since both lines have the same slope and different y-intercepts (\(-2\) for the solid line and \(7\) for the dashed line), they are parallel lines. Parallel lines do not intersect.

Since there is no point of intersection, the system of equations has 0 solutions.