Questions: Solve each system by substitution. 5) y=4x-9 y=x-3

Solve each system by substitution.
5)
y=4x-9
y=x-3
Transcript text: Solve each system by substitution. 5) \[ \begin{array}{l} y=4 x-9 \\ y=x-3 \end{array} \]
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Solution

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Solution Steps

Step 1: Write the System of Equations

We start with the given system of equations: \[ \begin{align_} y &= 4x - 9 \quad (1) \\ y &= x - 3 \quad (2) \end{align_} \]

Step 2: Set the Equations Equal

Since both equations equal \( y \), we can set them equal to each other: \[ 4x - 9 = x - 3 \]

Step 3: Solve for \( x \)

Rearranging the equation to isolate \( x \): \[ 4x - x = -3 + 9 \\ 3x = 6 \\ x = \frac{6}{3} = 2 \]

Step 4: Substitute \( x \) Back to Find \( y \)

Now that we have \( x = 2 \), we substitute it back into either equation to find \( y \). Using equation (2): \[ y = 2 - 3 = -1 \]

Step 5: Write the Solution

The solution to the system of equations is: \[ \begin{align_} x &= 2 \\ y &= -1 \end{align_} \]

Final Answer

\(\boxed{(x, y) = (2, -1)}\)

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