Question

1. $2x - 8y = 4$\\$\frac{5}{2}x + y = 5$

Explanation:

Step1: Simplify the first equation

Divide the first equation \(2x - 8y = 4\) by 2, we get \(x - 4y = 2\), and then express \(x\) in terms of \(y\): \(x = 4y + 2\).

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

Substitute \(x = 4y + 2\) into the second equation \(\frac{5}{2}x + y = 5\). So we have \(\frac{5}{2}(4y + 2)+y = 5\).
First, expand the left - hand side: \(\frac{5}{2}\times4y+\frac{5}{2}\times2 + y=5\), which simplifies to \(10y + 5 + y=5\).
Combine like terms: \(11y+5 = 5\).
Subtract 5 from both sides: \(11y=5 - 5=0\), so \(y = 0\).

Step3: Find the value of \(x\)

Substitute \(y = 0\) into \(x = 4y+2\), we get \(x=4\times0 + 2=2\).

Answer:

The solution of the system of equations is \(x = 2,y = 0\)