Question

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

Answer 1

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.