Question

use the substitution method to solve the system of equations. choose the correct ordered pair.
x+2y = 12
y = x + 3
a. (2, 1)
b. (5, 2)
c. (2, 5)
d. (5, 8)

Explanation:

Step1: Substitute \( y = x + 3 \) into \( x + 2y = 12 \)

Substitute \( y \) in the first equation with \( x + 3 \), we get \( x + 2(x + 3)=12 \).

Step2: Simplify and solve for \( x \)

Expand the left - hand side: \( x+2x + 6 = 12 \).
Combine like terms: \( 3x+6 = 12 \).
Subtract 6 from both sides: \( 3x=12 - 6=6 \).
Divide both sides by 3: \( x=\frac{6}{3}=2 \).

Step3: Find the value of \( y \)

Substitute \( x = 2 \) into \( y=x + 3 \), we get \( y=2 + 3=5 \).

Answer:

C. (2, 5)