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The image provides several algebraic equations where you're asked to substitute the given value of \( x \) and solve for \( y \). Let's go through the problems one by one:

### 1. Equation: \( 7x - 3y = 6 \); \( x = 3 \)
Substitute \( x = 3 \) into the equation:

\[
7(3) - 3y = 6 \implies 21 - 3y = 6
\]

Now solve for \( y \):

\[
21 - 6 = 3y \implies 15 = 3y \implies y = \frac{15}{3} = 5
\]

**Solution:** \( y = 5 \)

---

### 2. Equation: \( 6x + 5y = -7 \); \( x = -2 \)
Substitute \( x = -2 \) into the equation:

\[
6(-2) + 5y = -7 \implies -12 + 5y = -7
\]

Now solve for \( y \):

\[
5y = -7 + 12 \implies 5y = 5 \implies y = \frac{5}{5} = 1
\]

**Solution:** \( y = 1 \)

---

### 3. Equation: \( xy = 12 + 3x \); \( x = 4 \)
Substitute \( x = 4 \) into the equation:

\[
4y = 12 + 3(4) \implies 4y = 12 + 12 \implies 4y = 24
\]

Now solve for \( y \):

\[
y = \frac{24}{4} = 6
\]

**Solution:** \( y = 6 \)

---

### 4. Equation: \( \frac{2}{3}x = 2y - \frac{2}{5} \); \( x = -9 \)
Substitute \( x = -9 \) into the equation:

\[
\frac{2}{3}(-9) = 2y - \frac{2}{5} \implies -6 = 2y - \frac{2}{5}
\]

Add \( \frac{2}{5} \) to both sides:

\[
-6 + \frac{2}{5} = 2y \implies \frac{-30}{5} + \frac{2}{5} = 2y \implies \frac{-28}{5} = 2y
\]

Now divide by 2:

\[
y = \frac{-28}{5 \times 2} = \frac{-28}{10} = \frac{-14}{5}
\]

**Solution:** \( y = \frac{-14}{5} \)

---

### 5. Equation: \( \frac{2}{3}y + \frac{1}{2}x = 1 \); \( x = 12 \)
Substitute \( x = 12 \) into the equation:

\[
\frac{2}{3}y + \frac{1}{2}(12) = 1 \implies \frac{2}{3}y + 6 = 1
\]

Now solve for \( y \):

\[
\frac{2}{3}y = 1 - 6 \implies \frac{2}{3}y = -5
\]

Multiply by \( \frac{3}{2} \) to solve for \( y \):

\[
y = -5 \times \frac{3}{2} = \frac{-15}{2}
\]

**Solution:** \( y = \frac{-15}{2} \)

---

### 6. Equation: \( x - 2y = 3xy + 1 \); \( x = -2 \)
Substitute \( x = -2 \) into the equation:

\[
-2 - 2y = 3(-2)y + 1 \implies -2 - 2y = -6y + 1
\]

Now, simplify and solve for \( y \):

\[
-2 - 2y = -6y + 1 \implies -2 - 1 = -6y + 2y \implies -3 = -4y
\]

Now divide by \( -4 \):

\[
y = \frac{-3}{-4} = \frac{3}{4}
\]

**Solution:** \( y = \frac{3}{4} \)

---

Would you like more details or have any questions about these solutions? Here are some related problems to consider:

1. Solve \( 5x - 4y = 12 \) when \( x = 2 \).
2. If \( 3x + y = 9 \) and \( x = -3 \), what is \( y \)?
3. Solve \( 4x - 3y = 15 \) when \( x = 5 \).
4. What is the value of \( y \) if \( 2x - 7y = -9 \) and \( x = 1 \)?
5. Given \( \frac{5}{2}y + 3x = 0 \) and \( x = 6 \), find \( y \).

### Tip:
When solving for one variable, simplify the equation step by step to isolate the variable of interest on one side of the equation.

Substitute the given value of x into the equation, then solve the equation for y.

Learn how to solve linear equations by substituting the given value of x into the equation and solving for y. The steps involve simplifying and isolating y. Suitable for students in Grades 8-10.

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