Question

practice exercises lesson 7.3b
solve the system of equation by substitution.
y = 3x - 17
2x - y = 11
(1, -14)
(2, -7)
(3, -8)
(6, 1)

Explanation:

Step1: Substitute \( y = 3x - 17 \) into \( 2x - y = 11 \)

Substitute \( y \) in the second equation: \( 2x - (3x - 17) = 11 \)

Step2: Simplify the equation

Simplify: \( 2x - 3x + 17 = 11 \) → \( -x + 17 = 11 \)

Step3: Solve for \( x \)

Subtract 17: \( -x = 11 - 17 \) → \( -x = -6 \) → \( x = 6 \)

Step4: Substitute \( x = 6 \) into \( y = 3x - 17 \)

Calculate \( y \): \( y = 3(6) - 17 = 18 - 17 = 1 \)
Wait, the original selected option is (1, -14), but our calculation gives (6, 1). Let's re - check the substitution.

Wait, the second equation is \( 2x - y = 11 \), substituting \( y = 3x - 17 \) gives \( 2x-(3x - 17)=11 \), which is \( 2x - 3x + 17 = 11 \), \( -x=11 - 17=-6 \), so \( x = 6 \). Then \( y = 3\times6-17 = 18 - 17 = 1 \). So the correct solution is (6, 1).

Answer:

D. (6, 1) (assuming the options are labeled as A. (1, - 14), B. (2, - 7), C. (3, - 8), D. (6, 1))