Question

Solve the system using substitution. y=8-x y=2-y(1 point) Responses Image with alt text: the ordered pair (5, 13) Image with alt text: the ordered pair (13, negative 5) Image with alt text: the ordered pair (3, 5)

Answer 1

To solve the system using substitution, we substitute one equation into the other equation and solve for the variable.

Given equations:
1) y = 8 - x
2) y = 2 - y

Substitute equation 2) into equation 1):
2 - y = 8 - x

Rearrange the equation:
y = 8 - x - 2

Combine like terms:
y = 6 - x

Now that we have an expression for y, we can substitute it back into equation 2):
6 - x = 2 - (6 - x)

Simplify the equation:
6 - x = 2 - 6 + x

Move variables to one side and constants to the other side:
6 + 6 = 2 + x + x
12 = 2x + 2

Move the constants to one side:
12 - 2 = 2x
10 = 2x

Divide by 2 to solve for x:
x = 5

Substitute the value of x into equation 1) to solve for y:
y = 8 - x
y = 8 - 5
y = 3

The solution to the system is the ordered pair (x, y) = (5, 3).

Therefore, the correct response is: Image with alt text: the ordered pair (5, 3)