Question

solve the following system of equations.
$-6x - 5y = -9$
$-3x + 4y = -24$
$x = \square$
$y = \square$

Explanation:

Step1: Eliminate x variable

Multiply the second equation by -2:
$$-2(-3x + 4y) = -2(-24)$$
$$6x - 8y = 48$$

Step2: Add to first equation

Add the new equation to the first original equation to eliminate $x$:
$$(-6x - 5y) + (6x - 8y) = -9 + 48$$
$$-13y = 39$$

Step3: Solve for y

Divide both sides by -13:
$$y = \frac{39}{-13} = -3$$

Step4: Substitute y into second equation

Plug $y=-3$ into $-3x + 4y = -24$:
$$-3x + 4(-3) = -24$$
$$-3x -12 = -24$$

Step5: Solve for x

Isolate $x$ by first adding 12 to both sides, then dividing by -3:
$$-3x = -24 + 12 = -12$$
$$x = \frac{-12}{-3} = 4$$

Answer:

$x = 4$
$y = -3$