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algebra

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**1. **Algebra Equations
Level 8

**3. **Solving simultaneous equations by elimination. Eliminating unknowns by adding the equations:
y + 2x = 19
3y – 2x = 17

**4. **Solving simultaneous equations by elimination. Eliminating unknowns by adding the equations:
y + 2x = 19
3y – 2x = 17

**5. **Substitute for y = 9 in equation (1) y + 2x = 19
-9 -9
=> (9) + 2x = 19
÷2 ÷2
=> 2x = 10
=> x = 5
Check in equation (2): 3 y – 2 x = 17

**6. **Eliminating unknowns by subtraction:
3x - 2y = 19
x - 2y = 9
÷2 ÷2
(1) – (2) => 2x = 10
x = 5

**7. **Substitute for x = 5 in equation (1) 3x – 2y = 19
=> 3(5) – 2y = 19
+2y +2y
=> 15 – 2y = 19
- 19 -19
=> 15 = 19 + 2y
÷2 ÷2
=> -4 = 2y
-2 = y

**8. **When the signs are different add the equations.
When the signs are the same subtract the equations.

**9. **Simultaneous equations with different coefficients:
y + 2x = 8
2y – x = 11

**10. **Simultaneous equations with different coefficients:
y + 2x = 8
2y – x = 11

**11. **Simultaneous equations with different coefficients:
y + 2x = 8
2y – x = 11

**12. **
y + 2x = 8 (1)
2y – x = 11 (2)