Question

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

0

1

2

infinite

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 set the two equations equal to each other to find the point of intersection:

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

Now, solve for \( x \):

\[
x + x = 5 - 5
\]

\[
2x = 0 \implies x = 0
\]

Next, we can substitute \( x = 0 \) back into either equation to find \( y \):

Using the first equation:

\[
y = 0 + 5 = 5
\]

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

Since we found exactly one point of intersection, this system of equations has exactly one solution.

Therefore, the answer is:

**1**