Question

1. 8x + 2y = 30; 7x + 2y = 24

Explanation:

Step1: Subtract the two equations

Subtract the second equation \(7x + 2y = 24\) from the first equation \(8x + 2y = 30\) to eliminate \(y\).
\[

$$\begin{align*} (8x + 2y) - (7x + 2y) &= 30 - 24\\ 8x + 2y - 7x - 2y &= 6\\ x &= 6 \end{align*}$$

\]

Step2: Substitute x into one equation

Substitute \(x = 6\) into the second equation \(7x + 2y = 24\) to find \(y\).
\[

$$\begin{align*} 7\times6 + 2y &= 24\\ 42 + 2y &= 24\\ 2y &= 24 - 42\\ 2y &= -18\\ y &= -9 \end{align*}$$

\]

Answer:

\(x = 6\), \(y = -9\)