Determine the number of solutions to this system of linear equations (0, 1, ∞):

Question

y=7x+8

−7x+y=−8

(1 point)
This system of linear equations has
solution(s).
Remaining Attempts : 3

Answer 1

To determine the number of solutions to the system of linear equations given by:

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

we can start by rewriting the second equation in a more convenient form. Rearranging the second equation gives us:

\[ y = 7x - 8 \]

Now we have the following two equations:

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

Next, we notice that both equations are in the form \( y = mx + b \), where \( m \) is the slope of the line. The slopes \( m \) for both equations are equal (both are 7), but the y-intercepts are different (8 for the first equation and -8 for the second equation).

Since the slopes are the same but the y-intercepts are different, these two lines are parallel and will never intersect. Therefore, there are no solutions to this system of equations.

In conclusion, the system has:

\[ \text{0 solutions.} \]