Question

find the solution to the system of equations. you can use the interactive graph below to find the solution. \\(\

$$\begin{cases} -2x + 2y = -4 \\\\ 3x + 3y = -18 \\end{cases}$$

\\) \\(x = \square\\) \\(y = \square\\)

Explanation:

Step1: Simplify first equation

Divide by -2:
$$x - y = 2$$
Rearrange to:
$$x = y + 2$$

Step2: Simplify second equation

Divide by 3:
$$x + y = -6$$

Step3: Substitute x into equation

Substitute $x = y + 2$ into $x + y = -6$:
$$(y + 2) + y = -6$$

Step4: Solve for y

Combine like terms, isolate y:
$$2y + 2 = -6$$
$$2y = -8$$
$$y = -4$$

Step5: Solve for x

Substitute $y=-4$ into $x = y + 2$:
$$x = -4 + 2 = -2$$

Answer:

$x = -2$
$y = -4$