One Solution, No Solution, or Many Solutions Practice

Question

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Question
Use the image to answer the 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 ∞
?

(1 point)
Remaining Attempts : 3
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page 19 of 21

Answer 1

To analyze the system of equations given:

1. The first equation is a line represented by \( y = 3x - 2 \).
2. The second equation is given as \( -3x + y = 7 \), which can be rearranged to \( y = 3x + 7 \).

Analyzing the Lines:

• The line from the first equation has a slope of 3.
• The line from the second equation also has a slope of 3.

Since both lines have the same slope (3), they are parallel.

Conclusion:

Parallel lines do not intersect, and therefore, they do not share any common points.

This means that the system of equations has 0 solutions.