Simple Algebra - Worksheet Digital - Free Printable

To solve the given algebraic equations and find the values of \( x \) and \( y \), we will solve each equation step by step. Let's go through each equation one by one.

Equation 1: \( x + 4 = 6 \)

1. Subtract 4 from both sides:
\[
x + 4 - 4 = 6 - 4
\]
\[
x = 2
\]

Equation 2: \( y - 4 = 8 \)

1. Add 4 to both sides:
\[
y - 4 + 4 = 8 + 4
\]
\[
y = 12
\]

Equation 3: \( y + 5 = 12 \)

1. Subtract 5 from both sides:
\[
y + 5 - 5 = 12 - 5
\]
\[
y = 7
\]

Equation 4: \( x - 4 = 3 \)

1. Add 4 to both sides:
\[
x - 4 + 4 = 3 + 4
\]
\[
x = 7
\]

Equation 5: \( x + 0 = 11 \)

1. Simplify (adding 0 does not change the value):
\[
x = 11
\]

Equation 6: \( y - 3 = 9 \)

1. Add 3 to both sides:
\[
y - 3 + 3 = 9 + 3
\]
\[
y = 12
\]

Equation 7: \( y + 3 = 15 \)

1. Subtract 3 from both sides:
\[
y + 3 - 3 = 15 - 3
\]
\[
y = 12
\]

Equation 8: \( x - 7 = 10 \)

1. Add 7 to both sides:
\[
x - 7 + 7 = 10 + 7
\]
\[
x = 17
\]

Equation 9: \( x + 6 = 24 \)

1. Subtract 6 from both sides:
\[
x + 6 - 6 = 24 - 6
\]
\[
x = 18
\]

Equation 10: \( y - 10 = 15 \)

1. Add 10 to both sides:
\[
y - 10 + 10 = 15 + 10
\]
\[
y = 25
\]

Summary of Solutions:

- From Equation 1: \( x = 2 \)
- From Equation 2: \( y = 12 \)
- From Equation 3: \( y = 7 \)
- From Equation 4: \( x = 7 \)
- From Equation 5: \( x = 11 \)
- From Equation 6: \( y = 12 \)
- From Equation 7: \( y = 12 \)
- From Equation 8: \( x = 17 \)
- From Equation 9: \( x = 18 \)
- From Equation 10: \( y = 25 \)

Each equation provides a different value for \( x \) or \( y \). Since the problem asks to find the values of \( x \) and \( y \), and there are multiple equations, we can conclude that the values of \( x \) and \( y \) vary depending on the specific equation. However, if we are to summarize the unique solutions:

- Possible values for \( x \): \( 2, 7, 11, 17, 18 \)
- Possible values for \( y \): \( 7, 12, 25 \)

If the task is to solve each equation individually, the solutions are as follows:

\[
\boxed{
\begin{aligned}
&x = 2, \quad y = 12 \\
&y = 7, \quad x = 7 \\
&x = 11, \quad y = 12 \\
&x = 17, \quad y = 25 \\
&x = 18, \quad y = 25
\end{aligned}
}
\]