Question

what is the solution of the system of equations?\

$$\begin{cases}13x - 6y = 2\\\\3x - 4y = -10\\end{cases}$$

\
enter your answer in the boxes.\
(\boxed{ }, \boxed{ })

Explanation:

Step1: Eliminate $x$ via scaling

Multiply first eq by 3, second by 13:
$3(13x - 6y) = 3(2) \implies 39x - 18y = 6$
$13(3x - 4y) = 13(-10) \implies 39x - 52y = -130$

Step2: Subtract equations to solve $y$

Subtract second new eq from first:
$(39x - 18y) - (39x - 52y) = 6 - (-130)$
$34y = 136$
$y = \frac{136}{34} = 4$

Step3: Substitute $y=4$ to find $x$

Use second original equation:
$3x - 4(4) = -10$
$3x - 16 = -10$
$3x = 6$
$x = \frac{6}{3} = 2$

Answer:

$(2, 4)$