Question

question 7 of 25
use the substitution method to solve the system of equations. choose the correct ordered pair.
2x + y = 8
y = -x + 5

a. (3, 2)
b. (2, 3)
c. (5, 0)
d. (4, 1)

Explanation:

Step1: Substitute \( y = -x + 5 \) into \( 2x + y = 8 \)

Substitute the expression for \( y \) from the second equation into the first equation. So we get \( 2x + (-x + 5) = 8 \).

Step2: Simplify and solve for \( x \)

Simplify the left - hand side of the equation: \( 2x - x+5 = 8 \), which simplifies to \( x + 5=8 \). Subtract 5 from both sides: \( x=8 - 5=3 \).

Step3: Substitute \( x = 3 \) into \( y=-x + 5 \)

Now that we know \( x = 3 \), substitute it into the equation \( y=-x + 5 \). So \( y=-3 + 5 = 2 \).

Answer:

A. (3, 2)