Question

What is the solution to the system of equations:

y=x−1
−x+y=2(1 point)
Responses

(1,0)open paren 1 comma 0 close paren

(0,2)open paren 0 comma 2 close paren

infinitely many solutions
infinitely many solutions

no solution

Answer 1

To solve the system of equations, we can use the method of substitution.

First, we can rewrite the second equation as:

-y = -2x + 2

Now, we can substitute the value of y from the first equation into the second equation:

-(x - 1) = -2x + 2

Expanding the parentheses:

-x + 1 = -2x + 2

Adding 2x to both sides:

x + 1 = 2

Subtracting 1 from both sides:

x = 1

Now that we have found the value of x, we can substitute it back into the first equation to find y:

y = x - 1
y = 1 - 1
y = 0

Therefore, the solution to the system of equations is (1, 0).

The correct response is: (1, 0) (or option 1).