Let’s solve each system of equations step by step. We’ll use the elimination method since all equations are set up nicely for it.
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Problem 1:
6b + 3a = 54
4b = 20
From the second equation:
4b = 20 → b = 20 ÷ 4 =
5
Plug b = 5 into the first equation:
6(5) + 3a = 54 → 30 + 3a = 54
3a = 54 - 30 = 24 → a = 24 ÷ 3 =
8
✔ Solution: a = 8, b = 5
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Problem 2:
g + 4x = 11
8x = 16
From the second equation:
8x = 16 → x = 16 ÷ 8 =
2
Plug x = 2 into the first equation:
g + 4(2) = 11 → g + 8 = 11
g = 11 - 8 =
3
✔ Solution: g = 3, x = 2
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Problem 3:
4a + 5c = 30
5a = 25
From the second equation:
5a = 25 → a = 25 ÷ 5 =
5
Plug a = 5 into the first equation:
4(5) + 5c = 30 → 20 + 5c = 30
5c = 30 - 20 = 10 → c = 10 ÷ 5 =
2
✔ Solution: a = 5, c = 2
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Problem 4:
2a + 5x = 15
4a = 20
From the second equation:
4a = 20 → a = 20 ÷ 4 =
5
Plug a = 5 into the first equation:
2(5) + 5x = 15 → 10 + 5x = 15
5x = 15 - 10 = 5 → x = 5 ÷ 5 =
1
✔ Solution: a = 5, x = 1
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Problem 5:
2b + 4c = 12
2b = 10
From the second equation:
2b = 10 → b = 10 ÷ 2 =
5
Plug b = 5 into the first equation:
2(5) + 4c = 12 → 10 + 4c = 12
4c = 12 - 10 = 2 → c = 2 ÷ 4 =
0.5
✔ Solution: b = 5, c = 0.5
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Problem 6:
4c + 7z = 31
5c = 25
From the second equation:
5c = 25 → c = 25 ÷ 5 =
5
Plug c = 5 into the first equation:
4(5) + 7z = 31 → 20 + 7z = 31
7z = 31 - 20 = 11 → z = 11 ÷ 7 ≈
1.571 (or 11/7 as a fraction)
✔ Solution: c = 5, z = 11/7
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Problem 7:
6b + 4z = 14
5b = 5
From the second equation:
5b = 5 → b = 5 ÷ 5 =
1
Plug b = 1 into the first equation:
6(1) + 4z = 14 → 6 + 4z = 14
4z = 14 - 6 = 8 → z = 8 ÷ 4 =
2
✔ Solution: b = 1, z = 2
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Problem 8:
2a + 6c = 14
5a = 5
From the second equation:
5a = 5 → a = 5 ÷ 5 =
1
Plug a = 1 into the first equation:
2(1) + 6c = 14 → 2 + 6c = 14
6c = 14 - 2 = 12 → c = 12 ÷ 6 =
2
✔ Solution: a = 1, c = 2
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Final Answer:
1. a = 8, b = 5
2. g = 3, x = 2
3. a = 5, c = 2
4. a = 5, x = 1
5. b = 5, c = 0.5
6. c = 5, z = 11/7
7. b = 1, z = 2
8. a = 1, c = 2
Parent Tip: Review the logic above to help your child master the concept of algebra basics worksheet.
