Question

use substitution to solve the system. 3x - 15 = y 4x + 3y = 7

Explanation:

Step1: Substitute \( y = 3x - 15 \) into the second equation.

We have the second equation \( 4x + 3y = 7 \). Replace \( y \) with \( 3x - 15 \), so it becomes \( 4x + 3(3x - 15) = 7 \).

Step2: Simplify and solve for \( x \).

First, expand the equation: \( 4x + 9x - 45 = 7 \). Combine like terms: \( 13x - 45 = 7 \). Add 45 to both sides: \( 13x = 7 + 45 = 52 \). Then divide both sides by 13: \( x = \frac{52}{13} = 4 \).

Step3: Substitute \( x = 4 \) into the first equation to find \( y \).

The first equation is \( y = 3x - 15 \). Substitute \( x = 4 \): \( y = 3(4) - 15 = 12 - 15 = -3 \).

Answer:

\( x = 4 \)
\( y = -3 \)