Questions: Solve the system of linear equations by substitution. 2x - y = 23 x - 9 = -1

Solve the system of linear equations by substitution. 2x - y = 23 x - 9 = -1
Transcript text: Solve the system of linear equations by substitution. \[ \begin{array}{l} 2 x-y=23 \\ x-9=-1 \end{array} \]
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Solution

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Solve the system of linear equations by substitution.

Solve the second equation for \( x \).

The second equation is \( x - 9 = -1 \). Add 9 to both sides to solve for \( x \): \[ x - 9 + 9 = -1 + 9 \implies x = 8. \]

Substitute \( x = 8 \) into the first equation to solve for \( y \).

The first equation is \( 2x - y = 23 \). Substitute \( x = 8 \): \[ 2(8) - y = 23 \implies 16 - y = 23. \] Subtract 16 from both sides: \[ -y = 7 \implies y = -7. \]

The solution to the system is \( \boxed{x = 8, y = -7} \).

The solution to the system is \( \boxed{x = 8, y = -7} \).

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