Question

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y = -4x + 2(x - 6)
y = -3x - 39

Explanation:

Step1: Simplify the first equation

First, we simplify \( y = -4x + 2(x - 6) \). Distribute the 2 in \( 2(x - 6) \) to get \( 2x - 12 \). Then combine like terms: \( -4x + 2x = -2x \), so the first equation becomes \( y = -2x - 12 \).
\[ y = -4x + 2x - 12 = -2x - 12 \]

Step2: Set the two equations equal

Now we have the system of equations:
\( y = -2x - 12 \)
\( y = -3x - 39 \)
Since both equal \( y \), we can set them equal to each other: \( -2x - 12 = -3x - 39 \).

Step3: Solve for x

Add \( 3x \) to both sides: \( -2x + 3x - 12 = -39 \), which simplifies to \( x - 12 = -39 \). Then add 12 to both sides: \( x = -39 + 12 = -27 \).
\[ x - 12 + 12 = -39 + 12 \]
\[ x = -27 \]

Step4: Solve for y

Substitute \( x = -27 \) into one of the original equations, say \( y = -3x - 39 \). Plug in \( x = -27 \): \( y = -3(-27) - 39 = 81 - 39 = 42 \).
\[ y = -3(-27) - 39 = 81 - 39 = 42 \]

Answer:

The solution to the system of equations is \( x = -27 \) and \( y = 42 \), or the ordered pair \( (-27, 42) \).