One Solution, No Solution, or Many Solutions Practice

Question

Complete this assessment to review what you've learned. It will not count toward your grade.
5 of 55 of 5 Items

Question
Solve the given system of linear equations by inspection. Enter 1 for one solution, 2 for no solution, or 3 for infinitely many solutions.

y=−3x+5


2y=−6x+10


(1 point)

Answer 1

To determine whether the given system of equations has one solution, no solution, or infinitely many solutions, we can compare the two equations:

1. The first equation is: \[ y = -3x + 5 \]

2. The second equation can be simplified. Start with: \[ 2y = -6x + 10 \] Dividing the entire equation by 2 gives: \[ y = -3x + 5 \]

Now, we can see that both equations are actually the same: \[ y = -3x + 5 \]

Since both equations represent the same line, they have infinitely many solutions (every point on that line is a solution).

Therefore, the answer is 3 for infinitely many solutions.