Question

1. \

$$\begin{cases} y = x - 1 \\\\ x + 4y = 16 \\end{cases}$$

Explanation:

Step1: Substitute \( y = x - 1 \) into \( x + 4y = 16 \)

We know that \( y \) in the second equation can be replaced with \( x - 1 \) from the first equation. So we get \( x + 4(x - 1) = 16 \).

Step2: Simplify the equation

First, expand the left - hand side: \( x+4x - 4=16 \). Then combine like terms: \( 5x-4 = 16 \). Add 4 to both sides of the equation: \( 5x=16 + 4=20 \).

Step3: Solve for \( x \)

Divide both sides of the equation \( 5x = 20 \) by 5, we have \( x=\frac{20}{5}=4 \).

Step4: Solve for \( y \)

Substitute \( x = 4 \) into the equation \( y=x - 1 \), then \( y=4 - 1 = 3 \).

Answer:

The solution of the system of equations is \( x = 4,y = 3 \) (or the ordered pair \((4,3)\)).