Question: Solve each system by substitution. 5) \( y = 4x - 9 \) \( y = x - 3 \) \( 4x - 9 = x - 3 \)…

Solve each system by substitution.

5. \( y = 4x - 9 \) \( y = x - 3 \)

\( 4x - 9 = x - 3 \) \( +3 \) \( +3 \)

Solution

To solve the system by substitution, we have: \[ \begin{cases} y = 4x - 9 & \\ y = x - 3 & \end{cases} \] Substitute \(y = x - 3\) into the first equation: \(4x - 9 = x - 3\) Subtract \(x\) from both sides: \[ 4x - x - 9 = -3 \] Simplify: \[ 3x - 9 = -3 \] Add 9 to both sides: \[ 3x = 6 \] Divide both sides by 3: \[ x = 2 \] Substitute \(x = 2\) back into \(y = x - 3\): \[ y = 2 - 3 \] Simplify: \[ y = -1 \] The solution is \(x = 2, y = -1\).