Question

solve the system of equations.

y = 6x - 27
y = 4x - 17
a. (-5, 3) \t\t\t\tc. (5, 3)
b. (-3, -5) \t\t\t\td. no solution

please select the best answer from the choices provided

a
b
c
d

Explanation:

Step1: Set the two equations equal

Since both equations are solved for \( y \), we can set \( 6x - 27 = 4x - 17 \).

Step2: Solve for \( x \)

Subtract \( 4x \) from both sides: \( 6x - 4x - 27 = 4x - 4x - 17 \), which simplifies to \( 2x - 27 = -17 \). Then add 27 to both sides: \( 2x - 27 + 27 = -17 + 27 \), so \( 2x = 10 \). Divide both sides by 2: \( x = \frac{10}{2} = 5 \).

Step3: Find \( y \)

Substitute \( x = 5 \) into one of the original equations, say \( y = 4x - 17 \). Then \( y = 4(5) - 17 = 20 - 17 = 3 \).

Answer:

c. \( (5, 3) \)