Question

find the solution of the system of equations.\\(-2x - y = 6\\)\\(-2x + 8y = -30\\)

Explanation:

Step1: Eliminate $x$ via subtraction

Subtract the first equation from the second:
$$(-2x + 8y) - (-2x - y) = -30 - 6$$
$$9y = -36$$

Step2: Solve for $y$

Divide both sides by 9:
$$y = \frac{-36}{9} = -4$$

Step3: Substitute $y=-4$ into first equation

Plug $y=-4$ into $-2x - y = 6$:
$$-2x - (-4) = 6$$
$$-2x + 4 = 6$$

Step4: Solve for $x$

Isolate $x$:
$$-2x = 6 - 4$$
$$-2x = 2$$
$$x = \frac{2}{-2} = -1$$

Answer:

$x=-1$, $y=-4$