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

Answer 1

To determine the number of solutions to this system of linear equations, we can set the equations equal to each other since they both equal y:

x + 5 = -x + 5

By moving the variables to one side of the equation and the constants to the other side, we get:

x + x = 5 - 5

Simplifying, we have:

2x = 0

Dividing both sides of the equation by 2, we find:

x = 0

Substituting this value of x into either of the equations, we find:

y = 0 + 5
y = 5

Therefore, the system has one solution: (0, 5).