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

y=−x+5
(1 point)
Responses

2
2

1
1

infinite
infinite

0

Answer 1

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

1. **y = x + 5**
2. **y = -x + 5**

Let's analyze the two equations.

First, we can set the two equations equal to each other to find any points of intersection:

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

Now, add \(x\) to both sides:

\[
x + x + 5 = 5
\]

This simplifies to:

\[
2x + 5 = 5
\]

Next, subtract 5 from both sides:

\[
2x = 0
\]

Now, divide both sides by 2:

\[
x = 0
\]

Now that we have \(x\), we can substitute \(x = 0\) back into either equation to find the corresponding \(y\):

Using the first equation:

\[
y = 0 + 5 = 5
\]

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

Since we found one unique solution where both lines intersect, the answer is:

**1**