Question

solve this system of equations by using elimination.

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$$\begin{cases} -9x - 4y = 1 \\\\ 3x + 3y = 3 \\end{cases}$$

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\\((?, \quad)\\)

Explanation:

Identify the system of equations

Using the Systems of Equations knowledge point

$$
LATEXBLOCK0
$$

Multiply Equation 2 to align coefficients

To eliminate the \(x\) terms, multiply Equation 2 by 3:

$$ 3 \cdot (3x + 3y) = 3 \cdot 3 \implies 9x + 9y = 9 \quad \text{(Equation 3)} $$

Add Equation 1 and Equation 3

Add the equations to eliminate \(x\):

$$
LATEXBLOCK1
$$

Substitute y back to solve for x

Substitute \(y = 2\) into Equation 2:

$$
LATEXBLOCK2
$$

Verify the solution

Check the values \(x = -1\) and \(y = 2\) in Equation 1:

$$ -9(-1) - 4(2) = 9 - 8 = 1 $$

The solution is correct.

Answer:

Solve this system of equations by using elimination.

$$
LATEXBLOCK0
$$

The solution is (<blank>-1</blank>, <blank>2</blank>).