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

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

we can analyze the equations.

1. The first equation \( y = x + 5 \) is a straight line with a slope of 1.
2. The second equation \( y = -x + 5 \) is a straight line with a slope of -1.

To find the point of intersection, we can set the two equations equal to each other:

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

Now, let's solve for \( x \):

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

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

\[
y = 0 + 5 = 5
\]

So, the point of intersection is \( (0, 5) \).

Since the two lines intersect at exactly one point, the system of equations has **one solution**.

**Final Answer: 1**