Simultaneous equations introduction Bar Model Silent Teacher Narration

Simultaneous equations introduction – Bar Model Silent Teacher Narration Practice Bar Model a a b Your Turn Total Equation Solution 8 2 a + 0 b = 8 a = 4 14 2 a + 1 b = 14 b = 6 Bar Model Total Equation Solution a a a 12 2 a + 0 b = 8 a = 4 a a a b 18 2 a + 1 b = 14 b = 6 Intelligent Practice

Worked Example @Mr. Gibbons Bar Model a a b Total Equation Solution ? =8 8 2 a + 0 b a =? 4 ? = 14 14 2 a + 1 b b =? 6 Your Turn Bar Model Total Equation Solution ? = 12 a a a 12 3 a + 0 b a =? 4 ? = 18 a a a b 18 3 a + 1 b b =? 6

Your Turn Worked Example @Mr. Gibbons Bar Model x x x y Total 18 16 Equation Solution ? = 18 3 x + 0 y x =? 6 ? = 16 2 x + 1 y y =? 4 Bar Model y y y x y y Total 12 14 Equation Solution ? = 12 0 x + 3 y x =? 6 ? = 14 1 x + 2 y y =? 4

@Mr. Gibbons Question Bar Model Total Equation Solution ? =2 2 1 x + 0 y x = 2? 8 1 x + 1 y y = 6? ? =8 1 x x y 2 x x y y 2 14 ? =2 1 x + 0 y x = 2? 1 x + 2 y ? = 14 y = 6 ? 3 x y 2 14 ? =2 1 x + 0 y x = 2? ? = 14 y = 6 ? 1 x + 2 y 4 x x y y x y 4 28 ? =4 2 x + 0 y x = 2? ? = 28 y = 6 ? 2 x + 4 y 5 x x y y x y 2 14 ? =2 2 x + 0 y x = 1? 2 x + 4 y ? = 14 y = 3 ?

Question @Mr. Gibbons 6 Bar Model Total Equation Solution ? = 20 x = ? 10 x x 20 2 x + 0 y y x y 140 2 x + 4 y? = 140 y = ? 30 7 ? = 60 x = ? 30 x x 60 2 x + 0 y x x y y 100 2 x + 4 y? = 100 y = ? 10 8 ? = 30 x = ? 30 x 30 1 x + 0 y x x y y 100 2 x + 4 y? = 100 y = ? 10 9 ? = 40 x = ? 30 x y 40 1 x + 1 y x x y y 100 2 x + 4 y? = 100 y = ? 10 10 x y x x y y 8 20 ? =8 1 x + 1 y x = ? 6 2 x + 4 y ? = 20 y = ? 2

Question @Mr. Gibbons 11 Bar Model Total Equation Solution ? = 16 x = ? 6 x x y y 16 2 x + 2 y x x y y 20 2 x + 4 y ? = 20 y = ? 2 12 x x y y 16 10 ? = 16 x = ? 6 2 x + 2 y 1 x + 2 y ? = 10 y = ? 2 13 x x y y 12 6 ? = 12 x = ? 6 2 x + 2 y ? =6 1 x + 2 y y = ? 0 14 x x y y 12 12 ? = 12 x = ? 0 2 x + 2 y ? = 12 y = ? 6 1 x + 2 y 15 x x y y x y 12 12 ? = 12 x = ? ? 2 x + 2 y 1 x + 1 y ? = 12 y = ? ?

Question @Mr. Gibbons 16 Bar Model x x y y x y Total Equation Solution ? = 12 x = ? ? 12 2 x + 2 y 6 1 x + ? 1 y = 6 y = ? ? 17 x x y y x y 0 0 2 x + ? 2 y = 0 1 x + ? 1 y = 0 x = ? ? y = ? ? 18 x x y y x x y 0 0 2 x + ? 2 y = 0 2 x + ? 1 y = 0 x = ? 0 y = ? 0 19 x x y y x x y 2 0 2 x + ? 2 y = 2 2 x + ? 1 y = 0 x = ? -1 y = ? 2 20 x x y y x y 2 0 2 x + ? 2 y = 2 1 x + ? 1 y = 0 x = ? ? y = ? ?

@Mr. Gibbons Q Equation Solution Q Equation 1 1 x + 0 y = 2 1 x + 1 y = 8 x= y= 2 1 x + 0 y = 2 1 x + 2 y = 14 3 Solution 2 6 11 2 x + 2 y = 16 2 x + 4 y = 20 x= y= 6 2 x= y= 2 6 12 2 x + 2 y = 16 1 x + 2 y = 10 x= y= 6 2 1 x + 0 y = 2 1 x + 2 y = 14 x= y= 2 6 13 2 x + 2 y = 12 1 x + 2 y = 6 x= y= 6 0 4 2 x + 0 y = 4 2 x + 4 y = 28 x= y= 2 6 14 2 x + 2 y = 12 1 x + 2 y = 12 x= y= 0 6 5 2 x + 0 y = 2 2 x + 4 y = 14 x= y= 1 3 15 2 x + 2 y = 12 1 x + 1 y = 12 x= y= ? ? no solutions! 6 2 x + 0 y = 20 2 x + 4 y = 140 x= y= 10 30 16 2 x + 2 y = 12 1 x + 1 y = 6 x= y= ? ? infinite solutions! 7 2 x + 0 y = 60 2 x + 4 y = 100 x= y= 30 10 17 2 x + 2 y = 0 1 x + 1 y = 0 x= y= ? ? infinite solutions! 8 1 x + 0 y = 30 2 x + 4 y = 100 x= y= 30 10 18 2 x + 2 y = 0 2 x + 1 y = 0 x= y= 0 0 9 1 x + 1 y = 40 2 x + 4 y = 100 x= y= 30 10 19 2 x + 2 y = 2 2 x + 1 y = 0 x= y= -1 2 10 1 x + 1 y = 8 2 x + 4 y = 20 x= y= 6 2 20 2 x + 2 y = 2 1 x + 1 y = 0 x= y= ? ? no solutions!