Determine the number of solutions to this system of linear equations:

Question

y=x+5
y=−x+5 (1 point)
Responses

1
1

infinite
infinite

0
0

2

Answer 1

The correct answer is 1 solution.

The two equations given are:

1) y = x + 5
2) y = -x + 5

From equation 1, we can rewrite it as x = y - 5.
Substituting this into equation 2 gives us:
y = -(y - 5) + 5

Simplifying this equation, we get:
y = -y + 10

Combining like terms, we have:
2y = 10

Simplifying further, we get:
y = 5

Substituting this value of y into equation 1 or 2 gives us:
5 = x + 5
x = 0

So the solution to the system of linear equations is x = 0, y = 5.

Since there is only one solution, the answer is 1.