Question

solve the system
3x - 4y = 12
2x + y = 8

Explanation:

Step1: Identify the system of equations

We have the system:

$$\begin{cases} 3x - 4y = 12 \\ 2x + y = 8 \end{cases}$$

Step2: Solve the second equation for \( y \)

From \( 2x + y = 8 \), we get \( y = 8 - 2x \).

Step3: Substitute \( y = 8 - 2x \) into the first equation

Substitute into \( 3x - 4y = 12 \):

$$ 3x - 4(8 - 2x) = 12 $$

Step4: Simplify and solve for \( x \)

Expand the left side:

$$ 3x - 32 + 8x = 12 $$

Combine like terms:

$$ 11x - 32 = 12 $$

Add 32 to both sides:

$$ 11x = 12 + 32 $$

$$ 11x = 44 $$

Divide both sides by 11:

$$ x = \frac{44}{11} = 4 $$

Step5: Substitute \( x = 4 \) back into \( y = 8 - 2x \) to find \( y \)

$$ y = 8 - 2(4) $$

$$ y = 8 - 8 = 0 $$

Answer:

The solution to the system is \( x = 4 \), \( y = 0 \)