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

Question

y=x+5

y=−x+5
(1 point)
Responses

0
0

1
1

2
2

infinite

Answer 1

To find the number of solutions to the system of equations given:

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

we can set these two equations equal to each other because they both equal \( y \).

Setting \( x + 5 = -x + 5 \):

1. \( x + 5 = -x + 5 \)
2. Adding \( x \) to both sides gives: \( 2x + 5 = 5 \)
3. Subtracting 5 from both sides gives: \( 2x = 0 \)
4. Dividing both sides by 2 gives: \( x = 0 \)

Now, we can substitute \( x = 0 \) back into either of the original equations to find \( y \):

Using \( y = x + 5 \):

• \( y = 0 + 5 = 5 \)

So, we have the solution \( (0, 5) \).

Since we found a unique solution to this system of equations, the number of solutions is 1.