Question

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

$$\begin{cases} -3x - 9y = 18 \\\\ 4x + 3y = 12 \\end{cases}$$

x = \boxed{} y = \boxed{}

Explanation:

Step1: Simplify the first equation

Divide the first equation \(-3x - 9y = 18\) by \(-3\), we get \(x + 3y = -6\), so \(x = -6 - 3y\).

Step2: Substitute into the second equation

Substitute \(x = -6 - 3y\) into the second equation \(4x + 3y = 12\). Then \(4(-6 - 3y) + 3y = 12\).
Expand it: \(-24 - 12y + 3y = 12\).
Combine like terms: \(-24 - 9y = 12\).
Add 24 to both sides: \(-9y = 36\).
Divide by \(-9\): \(y = -4\).

Step3: Find x

Substitute \(y = -4\) into \(x = -6 - 3y\), we get \(x = -6 - 3\times(-4) = -6 + 12 = 6\).

Answer:

\(x = 6\)
\(y = -4\)