One Solution, No Solution, or Many Solutions Practice

Question

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Question
Determine the number of solutions to this system of linear equations (0, 1, ∞)
:
y=3x−7

y=−2x+5
(1 point)
This system of linear equations has
solution(s).

Answer 1

To determine the number of solutions for the given system of linear equations, we can analyze the equations:

1. \( y = 3x - 7 \)
2. \( y = -2x + 5 \)

Since both equations are in the slope-intercept form \( y = mx + b \), we can find the slopes and the y-intercepts for each line.

For the first equation:

• Slope (m) = 3
• Y-intercept (b) = -7

For the second equation:

• Slope (m) = -2
• Y-intercept (b) = 5

Since the slopes of the two equations are different (3 and -2), the lines are not parallel and will intersect at one point.

Thus, this system of linear equations has one solution.

The answer is: This system of linear equations has 1 solution(s).