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=7x+8


−7x+y=−8


(1 point)
This system of linear equations has
solution(s).

Answer 1

To determine the number of solutions for the system of equations:

1. \( y = 7x + 8 \)
2. \( -7x + y = -8 \)

First, let's rewrite the second equation in slope-intercept form (y = mx + b).

Starting from: \[ -7x + y = -8 \] we can isolate \( y \): \[ y = 7x - 8 \]

Now we have the following two equations:

1. \( y = 7x + 8 \)
2. \( y = 7x - 8 \)

Both equations have the same slope (7) but different y-intercepts (8 and -8). Since they are parallel lines, they will never intersect.

Thus, this system of equations has no solutions.

So the answer is: 0 solutions.