Question

what is the solution for the system of equations?
$-5x - y = 21$
$-4x + y = 6$
$\circ$ $(5,1)$
$\circ$ $(3,6)$
$\circ$ $(-4,1)$
$\circ$ $(-3,-6)$

Explanation:

Step1: Label the two equations

Equation 1: $-5x - y = 21$
Equation 2: $-4x + y = 6$

Step2: Add equations to eliminate $y$

$$(-5x - y) + (-4x + y) = 21 + 6$$
$$-9x = 27$$

Step3: Solve for $x$

$$x = \frac{27}{-9} = -3$$

Step4: Substitute $x=-3$ into Equation 2

$$-4(-3) + y = 6$$
$$12 + y = 6$$

Step5: Solve for $y$

$$y = 6 - 12 = -6$$

Answer:

$(-3, -6)$