Question

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

y=−x+5

Responses

infinite
infinite - no response given

0
0 - no response given

2
2 - no response given

1
1 - correct
show your work

Answer 1

To determine the number of solutions, we can set the two equations equal to each other:

x + 5 = -x + 5

Add x to both sides:

2x + 5 = 5

Subtract 5 from both sides:

2x = 0

Divide by 2:

x = 0

Now that we have the value of x, we can substitute it back into one of the original equations to find y:

y = 0 + 5
y = 5

So the system of linear equations has one solution at (0, 5). Therefore, the correct response is 1.