Simultaneous Equations

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

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

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

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

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

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)

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

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)

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

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 –

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