To solve the system of equations using the substitution method, here are the steps:
1. Write down the given system of equations.
\( \begin{array}{l}
3x - y = 3 \quad \text{(Equation 1)} \\
y = 2x + 2 \quad \text{(Equation 2)}
\end{array} \)
2. Substitute Equation 2 into Equation 1.
Since Equation 2 gives \( y = 2x + 2 \), we can substitute \( 2x + 2 \) for \( y \) in Equation 1:
\( 3x - (2x + 2) = 3 \)
3. Simplify the equation obtained from the substitution.
\( 3x - 2x - 2 = 3 \)
Combine like terms:
\( x - 2 = 3 \)
4. Solve for \( x \).
Add 2 to both sides of the equation:
\( x - 2 + 2 = 3 + 2 \)
So:
\( x = 5 \)
5. Substitute \( x = 5 \) back into Equation 2 to solve for \( y \).
Equation 2 is \( y = 2x + 2 \). Substituting \( x = 5 \):
\( y = 2(5) + 2 \)
\( y = 10 + 2 \)
\( y = 12 \)
6. Write the solution as an ordered pair.
The solution to the system of equations is \( (x, y) = (5, 12) \).
Thus, the correct ordered pair is [tex]\( (5, 12) \)[/tex].
