Question

8 \

$$\begin{cases} 4x - y = 2 \\\\ 2x + 2y = 26 \\end{cases}$$

Explanation:

Step1: Solve the first equation for y

From \(4x - y = 2\), we can rewrite it as \(y = 4x - 2\).

Step2: Substitute y into the second equation

Substitute \(y = 4x - 2\) into \(2x + 2y = 26\), we get:
\[

$$\begin{align*} 2x + 2(4x - 2)&=26\\ 2x + 8x - 4&=26\\ 10x - 4&=26 \end{align*}$$

\]

Step3: Solve for x

Add 4 to both sides: \(10x = 26 + 4 = 30\)
Divide both sides by 10: \(x = \frac{30}{10} = 3\)

Step4: Substitute x back to find y

Substitute \(x = 3\) into \(y = 4x - 2\), we get \(y = 4\times3 - 2 = 12 - 2 = 10\)

Answer:

The solution to the system of equations is \(x = 3\) and \(y = 10\)