1. Simultaneous
Equations

2. You have already completed the bridging booklet
Reminder
You have already completed the bridging booklet
chapter 3 Simultaneous equations
- Elimination method
chapter 6 Quadratics
You will find solving simultaneous equations in almost every A level topic from indices to kinematics
Make sure you find a way to structure your work you are comfortable with and that you always check your answers
You MUST also be fluent at solving quadratics by factorising – this can also come up in many A level topics

3. Simultaneous equations
KUS objectives
BAT know and use three methods for solving simultaneous equations
Starter:
Solve
Solve
Solve

4. a) 𝒙 𝟐 −𝟓𝒙+𝟔=𝟎 b) 𝒙 𝟐 −𝟒𝒙=𝟏𝟐 c) 𝒙 𝟐 −𝟒𝒙−𝟐𝟏=𝟎 d) 𝟑𝒙 𝟐 −𝟒𝒙−𝟐𝟏=𝟎
WB3 Solve these quadratics by factorising
a) 𝒙 𝟐 −𝟓𝒙+𝟔=𝟎
b) 𝒙 𝟐 −𝟒𝒙=𝟏𝟐
c) 𝒙 𝟐 −𝟒𝒙−𝟐𝟏=𝟎
d) 𝟑𝒙 𝟐 −𝟒𝒙−𝟐𝟏=𝟎

5. WB 4 (a)
Solve the simultaneous equations below algebraically
𝒚= 𝟐𝒙+𝟖 And 𝒚=𝟕𝒙 −𝟐
𝑥 = 2
𝑦 =12

6. 𝑥 = 2 𝑥 = 3 𝑦 =0 𝑦 =3 𝒚= 𝒙 𝟐 −𝟐𝒙 And 𝒚=𝟑𝒙 −𝟔 𝒙 𝟐 −𝟐𝒙=𝟑𝒙 −𝟔 𝒙 𝟐 −𝟓𝒙+𝟔=𝟎
WB 4 (b)
Solve the simultaneous equations below algebraically
𝒚= 𝒙 𝟐 −𝟐𝒙 And 𝒚=𝟑𝒙 −𝟔
𝒙 𝟐 −𝟐𝒙=𝟑𝒙 −𝟔
𝒙 𝟐 −𝟓𝒙+𝟔=𝟎
𝒙−𝟐 𝒙−𝟑 =𝟎
𝑥 = 2
𝑥 = 3
𝑦 =0
𝑦 =3

7. WB4 Try these:
𝒄) 𝒚= 𝒙 𝟐 +𝟑 And
𝒚=𝟒𝒙+𝟐𝟒
𝒅) 𝒚= 𝒙 𝟐 −𝒙 And
𝒚=𝟑𝒙+𝟏𝟐
solutions
−𝟑, 𝟏𝟐 (𝟕, 𝟓𝟐)
solutions
𝟔, 𝟑𝟎 (−𝟐, 𝟔)

8. x = 2 or x = -2 y = 3 or y = 11 𝒚= 𝒙 𝟐 −𝟐𝒙+𝟑 And 𝒚+𝟐𝒙=𝟕
WB 5
Solve the simultaneous equations below algebraically
𝒚= 𝒙 𝟐 −𝟐𝒙+𝟑 And 𝒚+𝟐𝒙=𝟕
x = 2 or x = -2
y = 3 or y = 11

9. WB 5 Try these:
c) 𝒚= 𝟒+𝒙−𝒙 𝟐 And
𝟑𝒙+𝒚=𝟕
𝒃) 𝒚= 𝒙 𝟐 +𝟑𝒙−𝟖 And
𝒚−𝟐𝒙=𝟒
solutions
−𝟒, −𝟒 (𝟑, 𝟏𝟎)
solutions
𝟏, 𝟒 (𝟑, −𝟐)

10. Practice 1 a) f) b) g) c) h) d) i) e) j)

11. One thing to improve is –
KUS objectives BAT know and use three methods for solving simultaneous equations
self-assess
One thing learned is –
One thing to improve is –

12. END

13. Practice 2 a) f) b) g) c) h) d) i) e) j)