Question

solve this system of equations by using elimination.

\\\

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

\\

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

Explanation:

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<reasoning>

Identify the system of equations

Using the Systems of Equations knowledge point
\[

$$\begin{cases} -9x - 4y = 1 \quad \text{(Equation 1)} \\ 3x + 3y = 3 \quad \text{(Equation 2)} \end{cases}$$

\]

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 \(x\):
\[

$$\begin{aligned} (-9x - 4y) + (9x + 9y) &= 1 + 9 \\ 5y &= 10 \\ y &= 2 \end{aligned}$$

\]

Substitute y back to solve for x

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

$$\begin{aligned} 3x + 3(2) &= 3 \\ 3x + 6 &= 3 \\ 3x &= -3 \\ x &= -1 \end{aligned}$$

\]

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.
</reasoning>

<answer>
Solve this system of equations by using elimination.
\[

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

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

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</post_analysis>

Answer:

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<reasoning>

Identify the system of equations

Using the Systems of Equations knowledge point
\[

$$\begin{cases} -9x - 4y = 1 \quad \text{(Equation 1)} \\ 3x + 3y = 3 \quad \text{(Equation 2)} \end{cases}$$

\]

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 \(x\):
\[

$$\begin{aligned} (-9x - 4y) + (9x + 9y) &= 1 + 9 \\ 5y &= 10 \\ y &= 2 \end{aligned}$$

\]

Substitute y back to solve for x

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

$$\begin{aligned} 3x + 3(2) &= 3 \\ 3x + 6 &= 3 \\ 3x &= -3 \\ x &= -1 \end{aligned}$$

\]

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.
</reasoning>

<answer>
Solve this system of equations by using elimination.
\[

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

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

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