Let's solve each equation for
y step by step. The goal is to isolate
y on one side of the equation.
---
1) -2(x + 3y) = 18
Step 1: Distribute the -2:
$$
-2x - 6y = 18
$$
Step 2: Add $2x$ to both sides:
$$
-6y = 18 + 2x
$$
Step 3: Divide both sides by -6:
$$
y = \frac{18 + 2x}{-6} = -\frac{18}{6} - \frac{2x}{6} = -3 - \frac{1}{3}x
$$
✔ Answer: $ y = -\frac{1}{3}x - 3 $
---
2) 5x + 10 = 10y
Step 1: Divide both sides by 10:
$$
\frac{5x}{10} + \frac{10}{10} = y \Rightarrow \frac{1}{2}x + 1 = y
$$
✔ Answer: $ y = \frac{1}{2}x + 1 $
---
3) 5y + 8 = 2y - 3x + 5
Step 1: Move all terms with
y to one side, others to the other:
$$
5y - 2y = -3x + 5 - 8
\Rightarrow 3y = -3x - 3
$$
Step 2: Divide by 3:
$$
y = -x - 1
$$
✔ Answer: $ y = -x - 1 $
---
4) 3y + 15x = 12
Step 1: Subtract $15x$ from both sides:
$$
3y = 12 - 15x
$$
Step 2: Divide by 3:
$$
y = \frac{12}{3} - \frac{15x}{3} = 4 - 5x
$$
✔ Answer: $ y = -5x + 4 $
---
5) x = 5y - 10 + 2x
Step 1: Move all terms to one side:
$$
x - 2x = 5y - 10 \Rightarrow -x = 5y - 10
$$
Step 2: Add 10 to both sides:
$$
10 - x = 5y
$$
Step 3: Divide by 5:
$$
y = \frac{10 - x}{5} = 2 - \frac{1}{5}x
$$
✔ Answer: $ y = -\frac{1}{5}x + 2 $
---
6) 8x - 4y = 4
Step 1: Subtract $8x$ from both sides:
$$
-4y = 4 - 8x
$$
Step 2: Divide by -4:
$$
y = \frac{4 - 8x}{-4} = -1 + 2x
$$
✔ Answer: $ y = 2x - 1 $
---
7) 9x + 3y = 3
Step 1: Subtract $9x$ from both sides:
$$
3y = 3 - 9x
$$
Step 2: Divide by 3:
$$
y = 1 - 3x
$$
✔ Answer: $ y = -3x + 1 $
---
8) 5(x + y) = 20 + 3x
Step 1: Expand left side:
$$
5x + 5y = 20 + 3x
$$
Step 2: Subtract $5x$ from both sides:
$$
5y = 20 + 3x - 5x = 20 - 2x
$$
Step 3: Divide by 5:
$$
y = \frac{20 - 2x}{5} = 4 - \frac{2}{5}x
$$
✔ Answer: $ y = -\frac{2}{5}x + 4 $
---
9) 3y - 21 = 12x
Step 1: Add 21 to both sides:
$$
3y = 12x + 21
$$
Step 2: Divide by 3:
$$
y = 4x + 7
$$
✔ Answer: $ y = 4x + 7 $
---
10) 2x + 3y = 3
Step 1: Subtract $2x$:
$$
3y = 3 - 2x
$$
Step 2: Divide by 3:
$$
y = 1 - \frac{2}{3}x
$$
✔ Answer: $ y = -\frac{2}{3}x + 1 $
---
11) x - 2y = 4
Step 1: Subtract $x$:
$$
-2y = 4 - x
$$
Step 2: Divide by -2:
$$
y = \frac{4 - x}{-2} = -2 + \frac{1}{2}x
$$
✔ Answer: $ y = \frac{1}{2}x - 2 $
---
12) -2x - y = -3
Step 1: Add $2x$ to both sides:
$$
-y = 2x - 3
$$
Step 2: Multiply both sides by -1:
$$
y = -2x + 3
$$
✔ Answer: $ y = -2x + 3 $
---
✔ Final Answers:
| Problem | Answer |
|--------|--------|
| 1) | $ y = -\frac{1}{3}x - 3 $ |
| 2) | $ y = \frac{1}{2}x + 1 $ |
| 3) | $ y = -x - 1 $ |
| 4) | $ y = -5x + 4 $ |
| 5) | $ y = -\frac{1}{5}x + 2 $ |
| 6) | $ y = 2x - 1 $ |
| 7) | $ y = -3x + 1 $ |
| 8) | $ y = -\frac{2}{5}x + 4 $ |
| 9) | $ y = 4x + 7 $ |
| 10) | $ y = -\frac{2}{3}x + 1 $ |
| 11) | $ y = \frac{1}{2}x - 2 $ |
| 12) | $ y = -2x + 3 $ |
Let me know if you'd like these graphed or explained further!
Parent Tip: Review the logic above to help your child master the concept of solving for y worksheet.
