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
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.