To solve the system of equations using substitution, follow these steps:
1. Write down the equations:
[tex]\[
\begin{array}{l}
2c - d = -2 \quad \text{(Equation 1)} \\
4c + d = 20 \quad \text{(Equation 2)}
\end{array}
\][/tex]
2. Solve Equation 1 for [tex]\( d \)[/tex]:
[tex]\[
2c - d = -2 \implies d = 2c + 2
\][/tex]
3. Substitute [tex]\( d = 2c + 2 \)[/tex] into Equation 2:
[tex]\[
4c + (2c + 2) = 20
\][/tex]
4. Combine like terms:
[tex]\[
4c + 2c + 2 = 20 \implies 6c + 2 = 20
\][/tex]
5. Solve for [tex]\( c \)[/tex]:
[tex]\[
6c + 2 = 20 \implies 6c = 18 \implies c = 3
\][/tex]
6. Substitute [tex]\( c = 3 \)[/tex] back into the expression for [tex]\( d \)[/tex]:
[tex]\[
d = 2c + 2 \implies d = 2(3) + 2 \implies d = 6 + 2 \implies d = 8
\][/tex]
7. Write the solution as an ordered pair:
[tex]\[
(c, d) = (3, 8)
\][/tex]
8. Verify the solution:
Substitute [tex]\( c = 3 \)[/tex] and [tex]\( d = 8 \)[/tex] back into the original equations to ensure both are satisfied:
- For Equation 1: [tex]\( 2(3) - 8 = 6 - 8 = -2 \)[/tex] (True)
- For Equation 2: [tex]\( 4(3) + 8 = 12 + 8 = 20 \)[/tex] (True)
Since both equations are satisfied, the solution to the system of equations is [tex]\( (3, 8) \)[/tex].
Therefore, the correct answer is:
[tex]\[
(3, 8)
\][/tex]
