Question

Determine the number of solutions to this system of linear equations:
y = 3+5
y = -x + 5 (1 point)

Answer 1

First, let's simplify the first equation:

1. \( y = 3 + 5 \)
\[
y = 8
\]

Now, we have the following two equations:

1. \( y = 8 \)
2. \( y = -x + 5 \)

Next, we can substitute the value of \( y \) from the first equation into the second equation to find \( x \):

\[
8 = -x + 5
\]

Now, solve for \( x \):

1. Add \( x \) to both sides:
\[
8 + x = 5
\]

2. Subtract 5 from both sides:
\[
x = 5 - 8
\]
\[
x = -3
\]

Now we have a specific solution:

- \( x = -3 \)
- \( y = 8 \)

Thus, the system of equations has a unique solution at the point \((-3, 8)\).

Therefore, the number of solutions to the system of linear equations is **1**.