Question

1. \

$$\begin{cases} 4y = 2x - 8 \\\\ 5x - 4y = 20 \\end{cases}$$

Explanation:

Step1: Substitute 4y from first equation

The first equation is \(4y = 2x - 8\). Substitute \(4y\) into the second equation \(5x - 4y = 20\), we get \(5x-(2x - 8)=20\).

Step2: Simplify the equation

Simplify \(5x-(2x - 8)=20\): \(5x - 2x+8 = 20\), which is \(3x+8 = 20\).

Step3: Solve for x

Subtract 8 from both sides: \(3x=20 - 8=12\). Then divide by 3: \(x=\frac{12}{3}=4\).

Step4: Solve for y

Substitute \(x = 4\) into \(4y = 2x - 8\): \(4y=2\times4 - 8=8 - 8 = 0\), so \(y = 0\).

Answer:

\(x = 4\), \(y = 0\)