Free Printable Solving for Y Worksheets for Students - Free Printable

Problem: Solve for \( y \) in each equation.

#### 1. \( 3y = 15x - 12 \)

To solve for \( y \), divide both sides of the equation by 3:
\[
y = \frac{15x - 12}{3}
\]
Simplify the right-hand side:
\[
y = 5x - 4
\]

Answer: \( y = 5x - 4 \)

---

#### 2. \( 5x + 10 = 10y \)

To solve for \( y \), first isolate \( y \) by dividing both sides of the equation by 10:
\[
y = \frac{5x + 10}{10}
\]
Simplify the right-hand side:
\[
y = \frac{5x}{10} + \frac{10}{10}
\]
\[
y = \frac{x}{2} + 1
\]

Answer: \( y = \frac{x}{2} + 1 \)

---

#### 3. \( 3y - 21 = 12x \)

To solve for \( y \), first add 21 to both sides:
\[
3y = 12x + 21
\]
Next, divide both sides by 3:
\[
y = \frac{12x + 21}{3}
\]
Simplify the right-hand side:
\[
y = 4x + 7
\]

Answer: \( y = 4x + 7 \)

---

#### 4. \( 5y + 3 = 2y - 3x + 5 \)

To solve for \( y \), first isolate the \( y \)-terms on one side. Subtract \( 2y \) from both sides:
\[
5y - 2y + 3 = -3x + 5
\]
\[
3y + 3 = -3x + 5
\]
Next, subtract 3 from both sides:
\[
3y = -3x + 2
\]
Finally, divide both sides by 3:
\[
y = \frac{-3x + 2}{3}
\]
Simplify the right-hand side:
\[
y = -x + \frac{2}{3}
\]

Answer: \( y = -x + \frac{2}{3} \)

---

#### 5. \( -2(x + 3y) = 18 \)

First, distribute the \(-2\) on the left-hand side:
\[
-2x - 6y = 18
\]
Next, isolate the \( y \)-term. Add \( 2x \) to both sides:
\[
-6y = 2x + 18
\]
Then, divide both sides by \(-6\):
\[
y = \frac{2x + 18}{-6}
\]
Simplify the right-hand side:
\[
y = -\frac{x}{3} - 3
\]

Answer: \( y = -\frac{x}{3} - 3 \)

---

#### 6. \( 5(x + y) = 20 + 3x \)

First, distribute the 5 on the left-hand side:
\[
5x + 5y = 20 + 3x
\]
Next, isolate the \( y \)-term. Subtract \( 5x \) from both sides:
\[
5y = 20 + 3x - 5x
\]
\[
5y = 20 - 2x
\]
Finally, divide both sides by 5:
\[
y = \frac{20 - 2x}{5}
\]
Simplify the right-hand side:
\[
y = 4 - \frac{2x}{5}
\]

Answer: \( y = 4 - \frac{2x}{5} \)

---

#### 7. \( 2x + 3y = 3 \)

To solve for \( y \), first isolate the \( y \)-term. Subtract \( 2x \) from both sides:
\[
3y = 3 - 2x
\]
Next, divide both sides by 3:
\[
y = \frac{3 - 2x}{3}
\]
Simplify the right-hand side:
\[
y = 1 - \frac{2x}{3}
\]

Answer: \( y = 1 - \frac{2x}{3} \)

---

#### 8. \( x + 5y - 10 = 2x \)

First, simplify the equation by isolating the \( y \)-term. Subtract \( x \) from both sides:
\[
5y - 10 = 2x - x
\]
\[
5y - 10 = x
\]
Next, add 10 to both sides:
\[
5y = x + 10
\]
Finally, divide both sides by 5:
\[
y = \frac{x + 10}{5}
\]

Answer: \( y = \frac{x + 10}{5} \)

---

#### 9. \( 8x - 4y = -4 \)

To solve for \( y \), first isolate the \( y \)-term. Subtract \( 8x \) from both sides:
\[
-4y = -4 - 8x
\]
Next, divide both sides by \(-4\):
\[
y = \frac{-4 - 8x}{-4}
\]
Simplify the right-hand side:
\[
y = 1 + 2x
\]

Answer: \( y = 1 + 2x \)

---

#### 10. Explain in words how to solve: \( 4x - 6 + 2y = 2x - y \)

To solve for \( y \):

1. Combine like terms involving \( x \):
Subtract \( 2x \) from both sides:
\[
4x - 2x - 6 + 2y = -y
\]
Simplify:
\[
2x - 6 + 2y = -y
\]

2. Isolate the \( y \)-terms:
Add \( y \) to both sides:
\[
2x - 6 + 2y + y = 0
\]
Simplify:
\[
2x - 6 + 3y = 0
\]

3. Isolate \( y \):
Add 6 to both sides:
\[
2x + 3y = 6
\]
Subtract \( 2x \) from both sides:
\[
3y = 6 - 2x
\]
Divide both sides by 3:
\[
y = \frac{6 - 2x}{3}
\]
Simplify:
\[
y = 2 - \frac{2x}{3}
\]

Final Answer: \( y = 2 - \frac{2x}{3} \)

---

Final Answers:

\[
\boxed{
\begin{aligned}
1. & \quad y = 5x - 4 \\
2. & \quad y = \frac{x}{2} + 1 \\
3. & \quad y = 4x + 7 \\
4. & \quad y = -x + \frac{2}{3} \\
5. & \quad y = -\frac{x}{3} - 3 \\
6. & \quad y = 4 - \frac{2x}{5} \\
7. & \quad y = 1 - \frac{2x}{3} \\
8. & \quad y = \frac{x + 10}{5} \\
9. & \quad y = 1 + 2x \\
10. & \quad y = 2 - \frac{2x}{3}
\end{aligned}
}
\]