Question

question
find the solution of the system of equations.

$4x - 3y = -13$
$-x + 6y = -44$

Explanation:

Step1: Eliminate x variable

Multiply the second equation by 4:
$$4(-x + 6y) = 4(-44)$$
$$-4x + 24y = -176$$

Step2: Add to first equation

Add the new equation to $4x - 3y = -13$:
$$(4x - 3y) + (-4x + 24y) = -13 + (-176)$$
$$21y = -189$$

Step3: Solve for y

Divide both sides by 21:
$$y = \frac{-189}{21} = -9$$

Step4: Substitute y to find x

Plug $y=-9$ into $-x + 6y = -44$:
$$-x + 6(-9) = -44$$
$$-x - 54 = -44$$
$$-x = 10$$
$$x = -10$$

Answer:

$x=-10$, $y=-9$