Question

homework
solve each system. show all work.

1. **

$2y - 3x = 29$
$y = 4 - 2x$
**
$x - y = 3$
$x = 5 - y$

Explanation:

Step1: Substitute \( x = 5 - y \) into \( x - y = 3 \)

Substitute the expression for \( x \) from the second equation into the first equation. So we get \( (5 - y) - y = 3 \).

Step2: Simplify the equation

Simplify the left - hand side of the equation: \( 5 - y - y=3 \), which simplifies to \( 5 - 2y = 3 \).

Step3: Solve for \( y \)

Subtract 5 from both sides: \( 5-2y - 5=3 - 5 \), so \( - 2y=-2 \). Then divide both sides by - 2: \( \frac{-2y}{-2}=\frac{-2}{-2} \), we get \( y = 1 \).

Step4: Solve for \( x \)

Substitute \( y = 1 \) into \( x = 5 - y \), then \( x=5 - 1=4 \).

Answer:

The solution of the system of equations is \( x = 4,y = 1 \) or the ordered pair \( (4,1) \)