Question

select the correct answer.
solve the system of equations given below.
$y - 15 = 3x$
$-2x + 5y = -3$
a. $(-7,-6)$
b. $(-6,3)$
c. $(-3,6)$
d. $(-6,-3)$

Explanation:

Step1: Rewrite the first equation

From \( y - 15 = 3x \), we can rewrite it as \( y = 3x + 15 \).

Step2: Substitute \( y \) into the second equation

Substitute \( y = 3x + 15 \) into \( -2x + 5y = -3 \). So we have \( -2x + 5(3x + 15) = -3 \).

Step3: Simplify and solve for \( x \)

First, expand the equation: \( -2x + 15x + 75 = -3 \). Combine like terms: \( 13x + 75 = -3 \). Subtract 75 from both sides: \( 13x = -3 - 75 = -78 \). Then divide by 13: \( x = \frac{-78}{13} = -6 \).

Step4: Find \( y \) using \( x = -6 \)

Substitute \( x = -6 \) into \( y = 3x + 15 \). So \( y = 3(-6) + 15 = -18 + 15 = -3 \).

Answer:

D. \((-6, -3)\)