Question

How many solutions exist for the system, x + y = 1 and y = -x + 1?

no solution
one solution
infinitely many solutions

Answer 1

Solve the first equation for y; that is, put it in slope intercept form.

Answer 2

x+y=1

Since x does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting x from both sides.
y=-x+1

To find the slope and y intercept, use the y=mx+b formula where m=slope and b is the y intercept.
y=mx+b

Using the y=mx+b formula, m=-1 and b=1.
m=-1, b=1

Answer 3

x+y=1

Since x does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting x from both sides.
y=-x+1