Question

1. $4x + 2y = 10$

$x - y = 13$

Explanation:

Step1: Solve the second equation for x

From \( x - y = 13 \), we can express \( x \) as \( x = y + 13 \).

Step2: Substitute x into the first equation

Substitute \( x = y + 13 \) into \( 4x + 2y = 10 \):
\[

$$\begin{align*} 4(y + 13) + 2y &= 10\\ 4y + 52 + 2y &= 10\\ 6y + 52 &= 10 \end{align*}$$

\]

Step3: Solve for y

Subtract 52 from both sides:
\[
6y = 10 - 52 = -42
\]
Divide both sides by 6:
\[
y = \frac{-42}{6} = -7
\]

Step4: Solve for x

Substitute \( y = -7 \) into \( x = y + 13 \):
\[
x = -7 + 13 = 6
\]

Answer:

\( x = 6 \), \( y = -7 \)