Let’s solve each system of equations using substitution, one at a time.
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System 1:
Equations:
1) 2x – y = -13
2) x – 4y = -24
Step 1: Solve equation (2) for x.
x = 4y – 24
Step 2: Substitute into equation (1).
2(4y – 24) – y = -13
→ 8y – 48 – y = -13
→ 7y – 48 = -13
→ 7y = 35
→ y = 5
Step 3: Plug y = 5 back into x = 4y – 24
x = 4(5) – 24 = 20 – 24 = -4
✔ Solution: x = -4, y = 5
Check in original equations:
Eq1: 2(-4) – 5 = -8 – 5 = -13 ✔️
Eq2: -4 – 4(5) = -4 – 20 = -24 ✔️
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System 2:
Equations:
1) y + 4x = -22
2) -2x + y = 26
Step 1: Solve equation (1) for y.
y = -22 – 4x
Step 2: Substitute into equation (2).
-2x + (-22 – 4x) = 26
→ -2x – 22 – 4x = 26
→ -6x – 22 = 26
→ -6x = 48
→ x = -8
Step 3: Plug x = -8 into y = -22 – 4x
y = -22 – 4(-8) = -22 + 32 = 10
✔ Solution: x = -8, y = 10
Check:
Eq1: 10 + 4(-8) = 10 – 32 = -22 ✔️
Eq2: -2(-8) + 10 = 16 + 10 = 26 ✔️
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System 3:
Equations:
1) 5x + y = -19
2) y – x = 11 → y = x + 11
Step 1: Substitute y = x + 11 into equation (1).
5x + (x + 11) = -19
→ 6x + 11 = -19
→ 6x = -30
→ x = -5
Step 2: Find y = x + 11 = -5 + 11 = 6
✔ Solution: x = -5, y = 6
Check:
Eq1: 5(-5) + 6 = -25 + 6 = -19 ✔️
Eq2: 6 – (-5) = 6 + 5 = 11 ✔️
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System 4:
Equations:
1) 2x + y = 20 → y = 20 – 2x
2) 6x – 5y = 12
Step 1: Substitute y = 20 – 2x into equation (2).
6x – 5(20 – 2x) = 12
→ 6x – 100 + 10x = 12
→ 16x – 100 = 12
→ 16x = 112
→ x = 7
Step 2: y = 20 – 2(7) = 20 – 14 = 6
✔ Solution: x = 7, y = 6
Check:
Eq1: 2(7) + 6 = 14 + 6 = 20 ✔️
Eq2: 6(7) – 5(6) = 42 – 30 = 12 ✔️
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System 5:
Equations:
1) x = -3y – 14
2) 5y + 4x = -21
Step 1: Substitute x from equation (1) into equation (2).
5y + 4(-3y – 14) = -21
→ 5y – 12y – 56 = -21
→ -7y – 56 = -21
→ -7y = 35
→ y = -5
Step 2: Plug y = -5 into x = -3y – 14
x = -3(-5) – 14 = 15 – 14 = 1
✔ Solution: x = 1, y = -5
Check:
Eq1: x = -3(-5) – 14 = 15 – 14 = 1 ✔️
Eq2: 5(-5) + 4(1) = -25 + 4 = -21 ✔️
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System 6:
Equations:
1) x – 5y = -18 → x = 5y – 18
2) 4y + 3x = 41
Step 1: Substitute x = 5y – 18 into equation (2).
4y + 3(5y – 18) = 41
→ 4y + 15y – 54 = 41
→ 19y – 54 = 41
→ 19y = 95
→ y = 5
Step 2: x = 5(5) – 18 = 25 – 18 = 7
✔ Solution: x = 7, y = 5
Check:
Eq1: 7 – 5(5) = 7 – 25 = -18 ✔️
Eq2: 4(5) + 3(7) = 20 + 21 = 41 ✔️
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Final Answer:
System 1: x = -4, y = 5
System 2: x = -8, y = 10
System 3: x = -5, y = 6
System 4: x = 7, y = 6
System 5: x = 1, y = -5
System 6: x = 7, y = 5
Parent Tip: Review the logic above to help your child master the concept of systems of equations problems worksheet.
