Question

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solve the system by substitution.

$-x + 8y = 20$

$x = y + 8$

answer attempt 1 out of

Explanation:

Step1: Substitute \( x = y + 8 \) into the first equation

We have the first equation \( -x + 8y = 20 \). Substitute \( x \) with \( y + 8 \), so we get \( -(y + 8) + 8y = 20 \).

Step2: Simplify the equation

Expand the left - hand side: \( -y - 8+8y = 20 \). Combine like terms: \( 7y-8 = 20 \).

Step3: Solve for \( y \)

Add 8 to both sides of the equation: \( 7y-8 + 8=20 + 8 \), which simplifies to \( 7y=28 \). Then divide both sides by 7: \( y=\frac{28}{7}=4 \).

Step4: Solve for \( x \)

Since \( x = y + 8 \) and \( y = 4 \), substitute \( y = 4 \) into this equation: \( x=4 + 8=12 \).

Answer:

The solution to the system of equations is \( x = 12 \) and \( y = 4 \), or the ordered pair \( (12,4) \).