Solving Simultaneous Equations with Bar Models and Practice
This content covers the introduction to simultaneous equations, using bar models to represent equations, practicing solving simultaneous equations step-by-step, and providing worked examples for better understanding. It includes equations with various coefficients and multiple variables, followed by solutions and explanations. The content is designed to help improve skills in solving simultaneous equations through visual representation and practice.
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Simultaneous equations Simultaneous equations introduction introduction Bar Model Bar Model Silent Teacher Intelligent Practice Your Turn Narration Bar Model a a a a Total 8 14 Equation 2a + 0b = 8 2a + 1b = 14 Solution a = 4 b = 6 b Bar Model a a a a Total 12 18 Equation 2a + 0b = 8 2a + 1b = 14 Solution a = 4 b = 6 a a b Practice
Worked Example Worked Example Your Turn Your Turn Bar Model a a a a Total 8 14 Equation 2a + 0b = 8 2a + 1b = 14 ? Solution a = 4 b = 6 ? Bar Model a a a a Total 12 18 Equation 3a + 0b = 12 3a + 1b = 18 ? Solution a = 4 b = 6 ? ? ? ? ? a a b b @MrGibbons
Your Turn Your Turn Worked Example Worked Example Bar Model x x x x Total 18 16 Equation 3x + 0y = 18 2x + 1y = 16 ? Solution x = 6 y = 4 ? Bar Model y y x y Total 12 14 Equation 0x + 3y = 12 1x + 2y = 14 ? Solution x = 6 y = 4 ? x y y y ? ? ? ? @MrGibbons
Question Bar Model Total 2 8 Equation 1x + 0y = 2 1x + 1y = 8 ? Solution x = 2 y = 6 x x y ? ? 1 ? x x y y 2 14 1x + 0y = 2 1x + 2y = 14 y = 6 ? x = 2 ? ? 2 ? x y x y 2 14 1x + 0y = 2 1x + 2y = 14 y = 6 ? x = 2 ? ? 3 ? x y x y y x y x 4 28 2x + 0y = 4 2x + 4y = 28 y = 6 ? x = 2 ? ? 4 ? @MrGibbons x y x y y x y x 2 14 2x + 0y = 2 2x + 4y = 14 y = 3 ? x = 1 ? ? 5 ?
Question Bar Model Total 20 140 2x + 4y = 140 y = 30 ? Equation 2x + 0y = 20 ? Solution x = 10 x y x y y x y x ? 6 ? x x x x y y y y 60 100 2x + 4y = 100 y = 10 ? 2x + 0y = 60 ? x = 30 ? 7 ? x x x y y y y 30 100 2x + 4y = 100 y = 10 ? 1x + 0y = 30 ? x = 30 ? 8 ? x x x y y y y y 40 100 2x + 4y = 100 y = 10 ? 1x + 1y = 40 ? x = 30 ? 9 ? @MrGibbons x x x y y y y y 8 20 1x + 1y = 8 2x + 4y = 20 ? x = 6 y = 2 ? ? 10 ?
Question Bar Model x x y y x x y y y y Total 16 20 Equation 2x + 2y = 16 x = 6 2x + 4y = 20 y = 2 ? Solution ? ? 11 ? x x y y x 16 10 2x + 2y = 16 x = 6 1x + 2y = 10 y = 2 ? ? ? 12 y y ? x x y y x 12 6 2x + 2y = 12 x = 6 1x + 2y = 6 ? ? ? 13 y y y = 0 ? x x y y x 12 12 2x + 2y = 12 x = 0 1x + 2y = 12 y = 6 ? ? ? 14 y y ? @MrGibbons x x y y x 12 12 2x + 2y = 12 x = ? 1x + 1y = 12 y = ? ? ? ? 15 y ?
Question Bar Model x x y y x y Total 12 6 Equation 2x + 2y = 12 1x + 1y = 6 ? Solution x = ? y = ? ? ? 16 ? x x y y x 0 0 2x + 2y = 0 1x + 1y = 0 ? x = ? y = ? ? ? 17 y ? x x y y x x y 0 0 2x + 2y = 0 2x + 1y = 0 ? x = 0 y = 0 ? ? 18 ? x x y y x x y 2 0 2x + 2y = 2 2x + 1y = 0 ? x = -1 y = 2 ? ? 19 ? @MrGibbons x x y y x 2 0 2x + 2y = 2 1x + 1y = 0 ? x = ? y = ? ? ? 20 y ?
Q Equation Solution Q Equation Solution 1 1x + 0y = 2 1x + 1y = 8 x = y = 2 6 11 2x + 2y = 16 2x + 4y = 20 x = y = 6 2 2 1x + 0y = 2 1x + 2y = 14 x = y = 2 6 12 2x + 2y = 16 1x + 2y = 10 x = y = 6 2 3 1x + 0y = 2 1x + 2y = 14 x = y = 2 6 13 2x + 2y = 12 1x + 2y = 6 x = y = 6 0 4 2x + 0y = 4 2x + 4y = 28 x = y = 2 6 14 2x + 2y = 12 1x + 2y = 12 x = y = 0 6 5 2x + 0y = 2 2x + 4y = 14 x = y = 1 3 15 2x + 2y = 12 1x + 1y = 12 x = y = ? ? no solutions! 6 2x + 0y = 20 2x + 4y = 140 x = y = 10 30 16 2x + 2y = 12 1x + 1y = 6 x = y = ? ? infinite solutions! 7 2x + 0y = 60 2x + 4y = 100 x = y = 30 10 17 2x + 2y = 0 1x + 1y = 0 x = y = ? ? infinite solutions! 8 1x + 0y = 30 2x + 4y = 100 x = y = 30 10 18 2x + 2y = 0 2x + 1y = 0 x = y = 0 0 @MrGibbons 9 1x + 1y = 40 2x + 4y = 100 x = y = 30 10 19 2x + 2y = 2 2x + 1y = 0 x = y = -1 2 10 1x + 1y = 8 2x + 4y = 20 x = y = 6 2 20 2x + 2y = 2 1x + 1y = 0 x = y = ? ? no solutions!
