Simultaneous Equations Indices

Simultaneous equations KUS objectives BAT solve simultaneous equations from index problems WB8 Starter: Solve 3 𝑥−4 =27 2 𝑥+4 =128 10× −2 𝑥 =−320 8× 𝑥 −3 =1 3 𝑥 = 81 −1/2 8× 2 𝑥 = 4 5

Solve the following simultaneous equations to find a and b: WB 9 Solve the following simultaneous equations to find a and b: 𝒙 𝒂 𝟐 = 𝒙 𝟒 𝟐𝒃 and 𝒙 𝒂 = 𝒙 𝟑 𝒙 𝒃

WB 10

WB x Solutions Sim eqns 𝟏𝟔 𝒙 𝟖 𝒚 = 𝟏 𝟒 And 𝟒 𝒙 𝟐 𝒚 =𝟏𝟔 𝟒𝒙−𝟑𝒚=−𝟐 𝟐𝒙+ 𝒚 =𝟒 𝟒×𝟏𝟔 𝒙 = 𝟖 𝒚 𝟐 𝟐𝒙+𝒚 = 𝟐 𝟒 𝟐 𝟐+𝟒𝒙 = 𝟐 𝟑𝒚 𝟐𝒙+𝒚=𝟒 solution 𝟏, 𝟐 𝟐+𝟒𝒙=𝟑𝒚 𝟒 𝒂 𝟐 𝒃 =64 And 𝟖 𝒃 𝟐 𝒂 =𝟒 𝟑 𝟐 𝒂 Sim eqns 𝟐 𝟐𝒂+ 𝟏 𝟐 𝒃 =𝟐 𝟔 𝟐 𝟑𝒃−𝒂 =𝟐 𝟐+ 𝒂 𝟑 𝟒𝒂+ 𝒃=𝟏𝟐 −𝟒𝒂+𝟗𝒃 = 6 𝟐𝒂+ 𝟏 𝟐 𝒃 = 6 𝟑𝒃−𝒂 = 𝟐+ 𝒂 𝟑 solution 𝟓𝟏 𝟐𝟎 , 𝟗 𝟓 𝟒𝒂+𝒃=𝟏𝟐 𝟗𝒃−𝟒𝒂 = 6

𝟑 𝒄 𝟑 𝒅 =𝟐𝟕 And 𝟗 𝒄 𝟑 𝒅 = 𝟏 𝟑 WB x Solutions Sim eqns 𝒄−𝒅 =𝟑 𝟐𝒄+𝒅 =−𝟏 𝟑 𝒄−𝒅 =𝟑 𝟑 𝟑 𝟐𝒄+𝒅 =𝟑 −𝟏 solution 𝟐 𝟑 ,− 𝟕 𝟑 𝒄−𝒅 =𝟑 𝟐𝒄+𝒅 =−𝟏

MEDIUM – now write a slightly trickier one Chili Pepper Challenge - MILD – write me an easy question that is / leads to simultaneous equations MEDIUM – now write a slightly trickier one HOT !!!– now a really tough one! Best way to make up sim eqns Qs is to start with two numbers, then make the equations Now swap questions

One thing to improve is – KUS objectives BAT solve simultaneous equations from index problems self-assess One thing learned is – One thing to improve is –

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WB 8 Solve these: Sim eqns 𝟏𝟔 𝒙 𝟖 𝒚 = 𝟏 𝟒 And 𝟒 𝒙 𝟐 𝒚 =𝟏𝟔 𝟒𝒙−𝟑𝒚=−𝟐 𝟐𝒙+ 𝒚 =𝟒 𝟒×𝟏𝟔 𝒙 = 𝟖 𝒚 𝟐 𝟐𝒙+𝒚 = 𝟐 𝟒 𝟐 𝟐+𝟒𝒙 = 𝟐 𝟑𝒚 𝟐𝒙+𝒚=𝟒 solution 𝟏, 𝟐 𝟐+𝟒𝒙=𝟑𝒚 Try these: 𝟒 𝒂 𝟐 𝒃 And 𝟖 𝒃 𝟐 𝒂 =𝟒 𝟑 𝟐 𝒂 𝟑 𝒄 𝟑 𝒅 =𝟐𝟕 And 𝟗 𝒄 𝟑 𝒅 = 𝟏 𝟑 solutions 𝟓𝟏 𝟐𝟎 , 𝟗 𝟓 solutions 𝟐 𝟑 ,− 𝟕 𝟑