Question

select the correct answer.

find the solution to the system of equations given below using elimination.

\\
\

$$\begin{cases} 3x + 2y = -3 \\\\ 9x + 4y = 3 \\end{cases}$$

\\

\\(\bigcirc\\) \\(x = 3, y = -6\\)
\\(\bigcirc\\) \\(x = -6, y = 3\\)
\\(\bigcirc\\) \\(x = 3, y = 6\\)
\\(\bigcirc\\) \\(x = -6, y = -3\\)

Explanation:

🆕 New Concept Discovered: Solving systems by elimination
Adding or subtracting equations to cancel out a variable.

Step 1: Align and multiply equations

We have the system of equations:

$$
LATEXBLOCK0
$$

To eliminate the \(y\) terms, we can multiply Equation 1 by \(-2\) so that the coefficient of \(y\) becomes \(-4\), which is the opposite of the \(4\) in Equation 2.

$$ -2(3x + 2y) = -2(-3) \implies -6x - 4y = 6 $$

Step 2: Add the equations to eliminate \(y\)

Now, add this new equation to Equation 2:

$$
LATEXBLOCK1
$$

Solve for \(x\):

$$ x = 3 $$

Step 3: Substitute \(x\) back to find \(y\)

Substitute \(x = 3\) into Equation 1:

$$
LATEXBLOCK2
$$

Answer:

\(x = 3, y = -6\)