Question

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

$$\begin{cases} -7x - 2y = 14 \\\\ 6x + 6y = 18 \\end{cases}$$

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

Explanation:

Step1: Simplify the second equation

Divide the second equation by 6:
$$\frac{6x + 6y}{6} = \frac{18}{6}$$
$$x + y = 3$$
Rearrange to isolate $x$:
$$x = 3 - y$$

Step2: Substitute $x$ into first equation

Substitute $x=3-y$ into $-7x - 2y = 14$:
$$-7(3 - y) - 2y = 14$$
Expand and simplify:
$$-21 + 7y - 2y = 14$$
$$-21 + 5y = 14$$

Step3: Solve for $y$

Add 21 to both sides:
$$5y = 14 + 21$$
$$5y = 35$$
Divide by 5:
$$y = \frac{35}{5} = 7$$

Step4: Solve for $x$

Substitute $y=7$ into $x=3-y$:
$$x = 3 - 7 = -4$$

Answer:

$x = -4$
$y = 7$