Question

1. $-4x + y = 6$

$-5x - y = 21$

Explanation:

Step1: Add the two equations

To eliminate \( y \), we add the equations \( -4x + y = 6 \) and \( -5x - y = 21 \).

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Step2: Solve for \( x \)

Divide both sides of \( -9x = 27 \) by \( -9 \):

$$ x = \frac{27}{-9} = -3 $$

Step3: Substitute \( x = -3 \) into one of the original equations

Let's use the first equation \( -4x + y = 6 \). Substitute \( x = -3 \):

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Step4: Solve for \( y \)

Subtract 12 from both sides:

$$ y = 6 - 12 = -6 $$

Answer:

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