Question

\

$$\begin{cases}12x + 4y = 22 \\\\ 3x - 8y = -10\\end{cases}$$

Explanation:

Step1: Eliminate x or y. Multiply the second equation by 4:

$$4\times(3x - 8y)=4\times(-10)$$
$$12x - 32y = -40$$

Step2: Subtract the new second equation from the first equation:

$$(12x + 4y)-(12x - 32y)=22-(-40)$$
$$12x + 4y - 12x + 32y = 22 + 40$$
$$36y = 62$$

Step3: Solve for y:

$$y=\frac{62}{36}=\frac{31}{18}$$

Step4: Substitute y into the second original equation to find x:

$$3x - 8\times\frac{31}{18}=-10$$
$$3x-\frac{124}{9}=-10$$
$$3x=-10+\frac{124}{9}$$
$$3x=\frac{-90 + 124}{9}=\frac{34}{9}$$
$$x=\frac{34}{27}$$

Answer:

The solution to the system is \( x = \frac{34}{27} \), \( y = \frac{31}{18} \)