Question

solve the following system using the elimination method. enter your answer as an ordered pair in the form $(x,y)$.
$6x - 5y = 50$
$2x + 6y = -14$

Explanation:

Step1: Scale the second equation

Multiply eq2 by 3:
$$3(2x + 6y) = 3(-14) \implies 6x + 18y = -42$$

Step2: Subtract scaled eq2 from eq1

Eliminate $x$:
$$(6x - 5y) - (6x + 18y) = 50 - (-42)$$
$$6x -5y -6x -18y = 92$$
$$-23y = 92$$

Step3: Solve for $y$

Divide by -23:
$$y = \frac{92}{-23} = -4$$

Step4: Substitute $y$ into eq2

Solve for $x$:
$$2x + 6(-4) = -14$$
$$2x -24 = -14$$
$$2x = 10$$
$$x = 5$$

Answer:

$(5, -4)$