Question

Determine the number of solutions to this system of linear equations (0, 1, infinity):
y = 7x + 8
-7 + y = -8
(1 point)
This system of linear equations has

Answer 1

Let's analyze the given system of linear equations:

1. The first equation is:
\[
y = 7x + 8
\]

2. The second equation simplifies as follows:
\[
-7 + y = -8
\]
Adding 7 to both sides:
\[
y = -1
\]

Now we have the system:
1. \( y = 7x + 8 \)
2. \( y = -1 \)

To find the intersection of these two equations, we can set them equal to each other:
\[
7x + 8 = -1
\]

Solving for \( x \):
\[
7x = -1 - 8
\]
\[
7x = -9
\]
\[
x = -\frac{9}{7}
\]

Now substituting \( x = -\frac{9}{7} \) back into either equation to find \( y \):
Using \( y = -1 \):
\[
y = -1
\]

Thus, we have a single solution:
\[
\left(-\frac{9}{7}, -1\right)
\]

This means that the system of linear equations has exactly **one solution**.

Thus, the answer is **1**.