-
System 1:
- Equation A: `2x + 3y = -12`
- Equation B: `-x - 3y = 18`
- Add A and B: `(2x - x) + (3y - 3y) = -12 + 18` → `x = 6`
- Substitute `x = 6` into A: `2(6) + 3y = -12` → `12 + 3y = -12` → `3y = -24` → `y = -8`
- Solution: `(6, -8)`
-
System 2:
- Equation A: `x + 3y = 18`
- Equation B: `-x - 4y = -25`
- Add A and B: `(x - x) + (3y - 4y) = 18 - 25` → `-y = -7` → `y = 7`
- Substitute `y = 7` into A: `x + 3(7) = 18` → `x + 21 = 18` → `x = -3`
- Solution: `(-3, 7)`
-
System 3:
- Equation A: `x - y = 11`
- Equation B: `2x + y = 19`
- Add A and B: `(x + 2x) + (-y + y) = 11 + 19` → `3x = 30` → `x = 10`
- Substitute `x = 10` into A: `10 - y = 11` → `-y = 1` → `y = -1`
- Solution: `(10, -1)`
-
System 4:
- Equation A: `-6x + 5y = 1`
- Equation B: `6x + 4y = -10`
- Add A and B: `(-6x + 6x) + (5y + 4y) = 1 - 10` → `9y = -9` → `y = -1`
- Substitute `y = -1` into A: `-6x + 5(-1) = 1` → `-6x - 5 = 1` → `-6x = 6` → `x = -1`
- Solution: `(-1, -1)`
-
System 5:
- Equation A: `7x - y = -10`
- Equation B: `-7x + 5y = -6`
- Add A and B: `(7x - 7x) + (-y + 5y) = -10 - 6` → `4y = -16` → `y = -4`
- Substitute `y = -4` into A: `7x - (-4) = -10` → `7x + 4 = -10` → `7x = -14` → `x = -2`
- Solution: `(-2, -4)`
-
System 6:
- Equation A: `-7x - y = 13`
- Equation B: `8x + y = -14`
- Add A and B: `(-7x + 8x) + (-y + y) = 13 - 14` → `x = -1`
- Substitute `x = -1` into A: `-7(-1) - y = 13` → `7 - y = 13` → `-y = 6` → `y = -6`
- Solution: `(-1, -6)`
Parent Tip: Review the logic above to help your child master the concept of solving systems worksheet.
