Question

use the substitution method to solve the system of equations. choose the correct ordered pair.
y = 6x + 2
y = x + 17
a. (3, 20)
b. (2, 14)
c. (1, 17)
d. (0, 2)

Explanation:

Step1: Substitute y from second equation into first

Since \( y = x + 17 \) and \( y = 6x + 2 \), substitute \( y \) in the first equation with \( x + 17 \):
\( x + 17 = 6x + 2 \)

Step2: Solve for x

Subtract \( x \) from both sides:
\( 17 = 5x + 2 \)
Subtract 2 from both sides:
\( 15 = 5x \)
Divide by 5:
\( x = 3 \)

Step3: Find y using x = 3

Substitute \( x = 3 \) into \( y = x + 17 \):
\( y = 3 + 17 = 20 \)

Answer:

A. (3, 20)