Problem: Solve for \( y \) in each of the given equations by substituting the provided value of \( x \).
####
Step-by-Step Solution:
1.
Equation: \( y = 5x \) when \( x = 6 \)
- Substitute \( x = 6 \) into the equation:
\[
y = 5(6)
\]
- Perform the multiplication:
\[
y = 30
\]
2.
Equation: \( y = 3x - 5 \) when \( x = 10 \)
- Substitute \( x = 10 \) into the equation:
\[
y = 3(10) - 5
\]
- Perform the multiplication:
\[
y = 30 - 5
\]
- Perform the subtraction:
\[
y = 25
\]
3.
Equation: \( y = 2x \) when \( x = 5 \)
- Substitute \( x = 5 \) into the equation:
\[
y = 2(5)
\]
- Perform the multiplication:
\[
y = 10
\]
4.
Equation: \( y = x + 7 \) when \( x = 8 \)
- Substitute \( x = 8 \) into the equation:
\[
y = 8 + 7
\]
- Perform the addition:
\[
y = 15
\]
5.
Equation: \( y = 2x \) when \( x = -3 \)
- Substitute \( x = -3 \) into the equation:
\[
y = 2(-3)
\]
- Perform the multiplication:
\[
y = -6
\]
6.
Equation: \( y = x + 10 \) when \( x = 7 \)
- Substitute \( x = 7 \) into the equation:
\[
y = 7 + 10
\]
- Perform the addition:
\[
y = 17
\]
7.
Equation: \( y = 2x + 1 \) when \( x = 4 \)
- Substitute \( x = 4 \) into the equation:
\[
y = 2(4) + 1
\]
- Perform the multiplication:
\[
y = 8 + 1
\]
- Perform the addition:
\[
y = 9
\]
8.
Equation: \( y = x - 6 \) when \( x = 13 \)
- Substitute \( x = 13 \) into the equation:
\[
y = 13 - 6
\]
- Perform the subtraction:
\[
y = 7
\]
Final Answers:
\[
\boxed{
\begin{aligned}
1. & \quad y = 30 \\
2. & \quad y = 25 \\
3. & \quad y = 10 \\
4. & \quad y = 15 \\
5. & \quad y = -6 \\
6. & \quad y = 17 \\
7. & \quad y = 9 \\
8. & \quad y = 7 \\
\end{aligned}
}
\]
Parent Tip: Review the logic above to help your child master the concept of algebra substitution worksheet.
