Let’s solve each problem step by step. We’re solving for
y in every equation — that means we want to get
y alone on one side of the equals sign.
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1.) 3y = 15x - 12
Divide both sides by 3:
→ y = (15x)/3 - 12/3
→ y = 5x - 4
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2.) 5x + 10 = 10y
We want y alone, so divide both sides by 10:
→ y = (5x + 10)/10
Break it up:
→ y = 5x/10 + 10/10
→ y = (1/2)x + 1
Or you can write: y = 0.5x + 1
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3.) 3y - 21 = 12x
Add 21 to both sides:
→ 3y = 12x + 21
Divide by 3:
→ y = 4x + 7
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4.) 5y + 3 = 2y - 3x + 5
Get all y terms on left, others on right.
Subtract 2y from both sides:
→ 3y + 3 = -3x + 5
Subtract 3 from both sides:
→ 3y = -3x + 2
Divide by 3:
→ y = -x + 2/3
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5.) -2(x + 3y) = 18
First, distribute the -2:
→ -2x - 6y = 18
Now, isolate y. Add 2x to both sides:
→ -6y = 2x + 18
Divide by -6:
→ y = (2x)/(-6) + 18/(-6)
→ y = -1/3 x - 3
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6.) 5(x + y) = 20 + 3x
Distribute the 5:
→ 5x + 5y = 20 + 3x
Subtract 5x from both sides:
→ 5y = 20 - 2x
Divide by 5:
→ y = 4 - (2/5)x
Or: y = -0.4x + 4
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7.) 2x + 3y = 3
Subtract 2x from both sides:
→ 3y = -2x + 3
Divide by 3:
→ y = (-2/3)x + 1
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8.) x + 5y - 10 = 2x
Subtract x from both sides:
→ 5y - 10 = x
Add 10 to both sides:
→ 5y = x + 10
Divide by 5:
→ y = (1/5)x + 2
Or: y = 0.2x + 2
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9.) 8x - 4y = -4
Subtract 8x from both sides:
→ -4y = -8x - 4
Divide by -4:
→ y = 2x + 1
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10.) Explain in words how to solve: 4x - 6 + 2y = 2x - y
(Give the final answer)
Step-by-step explanation:
We need to get all the
y terms on one side and everything else on the other.
Start with:
4x - 6 + 2y = 2x - y
Step 1: Add
y to both sides to move the -y from the right to the left:
→ 4x - 6 + 3y = 2x
Step 2: Subtract
4x from both sides to move the 4x to the right:
→ -6 + 3y = -2x
Step 3: Add
6 to both sides to move the -6 to the right:
→ 3y = -2x + 6
Step 4: Divide everything by 3 to solve for y:
→ y = (-2/3)x + 2
Final Answer: y = -⅔x + 2
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Final Answer:
1.) y = 5x - 4
2.) y = ½x + 1
3.) y = 4x + 7
4.) y = -x + ⅔
5.) y = -⅓x - 3
6.) y = -⅖x + 4
7.) y = -⅔x + 1
8.) y = ⅕x + 2
9.) y = 2x + 1
10.) y = -⅔x + 2
Parent Tip: Review the logic above to help your child master the concept of solve for y worksheet.
