Question

1. \

$$\begin{cases} 3x + 8y = -5 \\\\ -2x + 2y = 18 \\end{cases}$$

Explanation:

Step1: Simplify the second equation

Divide the second equation \(-2x + 2y = 18\) by 2, we get \(-x + y = 9\), which can be rewritten as \(y = x + 9\).

Step2: Substitute \(y = x + 9\) into the first equation

Substitute \(y\) in \(3x + 8y = -5\) with \(x + 9\), we have \(3x + 8(x + 9) = -5\).
Expand the left side: \(3x + 8x + 72 = -5\).
Combine like terms: \(11x + 72 = -5\).
Subtract 72 from both sides: \(11x = -5 - 72 = -77\).
Divide both sides by 11: \(x = -7\).

Step3: Find the value of \(y\)

Substitute \(x = -7\) into \(y = x + 9\), we get \(y = -7 + 9 = 2\).

Answer:

The solution of the system of equations is \(x = -7\), \(y = 2\)