Question

1. ( x + 2y = -1 )

( 2x - 3y = 12 )

Explanation:

Step1: Solve the first equation for x

From \( x + 2y = -1 \), we can express \( x \) as \( x = -1 - 2y \).

Step2: Substitute x into the second equation

Substitute \( x = -1 - 2y \) into \( 2x - 3y = 12 \):

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Step3: Solve for y

Add 2 to both sides:

$$ -7y = 12 + 2 = 14 $$

Divide both sides by -7:

$$ y = \frac{14}{-7} = -2 $$

Step4: Substitute y back to find x

Substitute \( y = -2 \) into \( x = -1 - 2y \):

$$ x = -1 - 2(-2) = -1 + 4 = 3 $$

Answer:

The solution to the system of equations is \( x = 3 \), \( y = -2 \)