Question

solve the following system using the elimination method.
$6x - 5y = 17$
$2x + 6y = -2$

Explanation:

Step1: Eliminate $x$ via scaling

Multiply the second equation by 3:
$$3(2x + 6y) = 3(-2) \implies 6x + 18y = -6$$

Step2: Subtract equations to remove $x$

Subtract the first equation from the scaled second equation:
$$(6x + 18y) - (6x - 5y) = -6 - 17$$
$$6x + 18y - 6x + 5y = -23$$
$$23y = -23$$

Step3: Solve for $y$

Divide both sides by 23:
$$y = \frac{-23}{23} = -1$$

Step4: Substitute $y=-1$ to find $x$

Use the second original equation $2x + 6y = -2$:
$$2x + 6(-1) = -2$$
$$2x - 6 = -2$$
$$2x = -2 + 6 = 4$$
$$x = \frac{4}{2} = 2$$

Answer:

$x=2$, $y=-1$