Question

solve the system of equations using elimination: $4x + 3y = -11$ and $-9x - 9y = 18$.

Explanation:

Step1: Simplify the second equation

Divide $-9x -9y =18$ by $-9$:
$$\frac{-9x}{-9} + \frac{-9y}{-9} = \frac{18}{-9}$$
$$x + y = -2$$

Step2: Scale the simplified equation

Multiply $x + y = -2$ by 3 to align $y$-terms:
$$3(x + y) = 3(-2)$$
$$3x + 3y = -6$$

Step3: Eliminate $y$ via subtraction

Subtract $3x + 3y = -6$ from $4x + 3y = -11$:
$$(4x + 3y) - (3x + 3y) = -11 - (-6)$$
$$4x + 3y -3x -3y = -11 +6$$
$$x = -5$$

Step4: Solve for $y$

Substitute $x=-5$ into $x + y = -2$:
$$-5 + y = -2$$
$$y = -2 +5$$
$$y=3$$

Answer:

$x=-5$, $y=3$