Question

solve the system of equations: 5x - 9y = 12; x + y = -6

Explanation:

Step1: Solve the system of equations

We have the system of equations:

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From the second equation \(x + y = -6\), we can express \(x\) as \(x = -6 - y\).

Step2: Substitute \(x\) into the first equation

Substitute \(x = -6 - y\) into \(5x - 9y = 12\):

$$ 5(-6 - y) - 9y = 12 $$

Expand the left side:

$$ -30 - 5y - 9y = 12 $$

Combine like terms:

$$ -30 - 14y = 12 $$

Step3: Solve for \(y\)

Add 30 to both sides:

$$ -14y = 12 + 30 $$

$$ -14y = 42 $$

Divide both sides by -14:

$$ y = \frac{42}{-14} = -3 $$

Step4: Solve for \(x\)

Substitute \(y = -3\) into \(x = -6 - y\):

$$ x = -6 - (-3) = -6 + 3 = -3 $$

Answer:

The solution to the system of equations is \(x = -3\) and \(y = -3\).