Question

Question
Determine the number of solutions to this system of linear equations:
y=x+5

y=−x+5
(1 point)
Responses

1
1

infinite
infinite

0
0

2

Answer 1

To solve the system of linear equations given by:

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

we can set these equations equal to each other, since they both equal \( y \):

\[
x + 5 = -x + 5
\]

Next, we'll solve for \( x \):

\[
x + x = 5 - 5
\]
\[
2x = 0
\]
\[
x = 0
\]

Now that we have \( x = 0 \), we can substitute this back into either of the original equations to find \( y \). We'll use the first equation:

\[
y = 0 + 5 = 5
\]

So, the solution to the system is \( (0, 5) \).

Since we found one unique solution to the system of linear equations, the number of solutions is:

**1.**