Question

7x - 4y = 26\
3x + 4y = -6

Explanation:

Step1: Add the two equations

To eliminate \( y \), we add the equations \( 7x - 4y = 26 \) and \( 3x + 4y = -6 \) together.
\[

$$\begin{align*} (7x - 4y) + (3x + 4y) &= 26 + (-6)\\ 7x - 4y + 3x + 4y &= 20\\ 10x &= 20 \end{align*}$$

\]

Step2: Solve for \( x \)

Divide both sides of the equation \( 10x = 20 \) by 10.
\[
x=\frac{20}{10}=2
\]

Step3: Substitute \( x = 2 \) into one of the original equations

Let's substitute \( x = 2 \) into the second equation \( 3x + 4y = -6 \).
\[

$$\begin{align*} 3(2)+4y&=-6\\ 6 + 4y&=-6 \end{align*}$$

\]

Step4: Solve for \( y \)

Subtract 6 from both sides:
\[
4y=-6 - 6=-12
\]
Divide both sides by 4:
\[
y=\frac{-12}{4}=-3
\]

Answer:

The solution to the system of equations is \( x = 2 \) and \( y=-3 \)