Questions: Use substitution to solve the system. 2x - 8 = y 3x + 2y = -2 x = y =

Use substitution to solve the system. 2x - 8 = y 3x + 2y = -2 x = y =
Transcript text: Use substitution to solve the system. \[ \begin{array}{c} 2 x-8=y \\ 3 x+2 y=-2 \end{array} \] \[ x= \] \[ y= \]
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Solution

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Solution Steps

Step 1: Substitute \( y \) from the first equation into the second equation

From the first equation, \( y = 2x - 8 \). Substitute this expression for \( y \) into the second equation: \[ 3x + 2(2x - 8) = -2 \]

Step 2: Simplify the equation

Expand and simplify the equation: \[ 3x + 4x - 16 = -2 \] \[ 7x - 16 = -2 \]

Step 3: Solve for \( x \)

Add 16 to both sides of the equation: \[ 7x = 14 \] Divide both sides by 7: \[ x = 2 \]

Step 4: Solve for \( y \)

Substitute \( x = 2 \) back into the first equation to find \( y \): \[ y = 2(2) - 8 \] \[ y = 4 - 8 \] \[ y = -4 \]

Final Answer

\[ x = \boxed{2} \] \[ y = \boxed{-4} \]

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