Question

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

y=−x+5
(1 point)
Responses

1
1

0
0

2
2

infinite

Answer 1

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

1. **First Equation**: \( y = x + 5 \)
2. **Second Equation**: \( y = -x + 5 \)

We can solve this by setting the two equations equal to each other since both equal \( y \):

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

Next, we can simplify this equation:

1. Add \( x \) to both sides:
\[
x + x + 5 = 5
\]
\[
2x + 5 = 5
\]

2. Subtract 5 from both sides:
\[
2x = 0
\]

3. Divide by 2:
\[
x = 0
\]

Now, we can find the corresponding \( y \) value by substituting \( x = 0 \) back into either of the original equations. We will use the first equation:

\[
y = 0 + 5 = 5
\]

So we have found one solution: \( (0, 5) \).

Since the two equations represent two lines that intersect at this point, the system has exactly one solution.

Therefore, the answer is:

**1**