Determine the number of solutions to this system of linear equations:
y=x+5
y=-x+5
The system of linear equations given is:
y = x + 5
y = -x + 5
We can solve this system by equating the two equations:
x + 5 = -x + 5
Adding x to both sides:
2x + 5 = 5
Subtracting 5 from both sides:
2x = 0
Dividing both sides by 2:
x = 0
Now that we have the value for x, we can substitute it back into either of the equations to solve for y. Let's substitute it into the first equation:
y = 0 + 5
y = 5
Therefore, the solution to the system of linear equations is x = 0 and y = 5.
Since this is the only solution, the number of solutions to the system is 1.