Question

lin is solving this system of equations:
\

$$\begin{cases} 6x - 5y = 34 \\\\ 3x + 2y = 8 \\end{cases}$$

Explanation:

Step1: Eliminate $x$ variable

Multiply the second equation by 2:
$2\times(3x + 2y) = 2\times8$
$6x + 4y = 16$

Step2: Subtract new eq from first eq

Subtract $6x + 4y = 16$ from $6x - 5y = 34$:
$(6x - 5y) - (6x + 4y) = 34 - 16$
$-9y = 18$

Step3: Solve for $y$

Divide both sides by $-9$:
$y = \frac{18}{-9} = -2$

Step4: Substitute $y=-2$ to find $x$

Plug $y=-2$ into $3x + 2y = 8$:
$3x + 2\times(-2) = 8$
$3x - 4 = 8$
$3x = 12$
$x = \frac{12}{3} = 4$

Answer:

$x=4$, $y=-2$