11X1 T01 08 simultaneous equations (2011)

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<ul><li> 1. Simultaneous Equations</li></ul> <p> 2. Simultaneous Equations 1) Eliminate a variable 3. Simultaneous Equations 1) Eliminate a variable 2) Solve for the other variable 4. Simultaneous Equations 1) Eliminate a variable 2) Solve for the other variable 3) Substitute to find the eliminated variable 5. Simultaneous Equations1) Eliminate a variable2) Solve for the other variable3) Substitute to find the eliminated variablee.g. (i ) 2 x 3 y 21 (1)5 x 2 y 3 (2) 6. Simultaneous Equations1) Eliminate a variable2) Solve for the other variable3) Substitute to find the eliminated variablee.g. (i ) 2 x 3 y 21 (1) 5 x 2 y 3 (2) Multiply (1) by 2 and (2) by 3 7. Simultaneous Equations1) Eliminate a variable2) Solve for the other variable3) Substitute to find the eliminated variablee.g. (i ) 2 x 3 y 21 (1) 5 x 2 y 3 (2) Multiply (1) by 2 and (2) by 34 x 6 y 42 15 x 6 y 9 8. Simultaneous Equations1) Eliminate a variable2) Solve for the other variable3) Substitute to find the eliminated variablee.g. (i ) 2 x 3 y 21 (1) 5 x 2 y 3 (2) Multiply (1) by 2 and (2) by 34 x 6 y 42 15 x 6 y 9 11x = 33 9. Simultaneous Equations1) Eliminate a variable2) Solve for the other variable3) Substitute to find the eliminated variablee.g. (i ) 2 x 3 y 21 (1) 5 x 2 y 3 (2) Multiply (1) by 2 and (2) by 34 x 6 y 42 15 x 6 y 9 11x = 33 x = 3 10. Simultaneous Equations1) Eliminate a variable2) Solve for the other variable3) Substitute to find the eliminated variablee.g. (i ) 2 x 3 y 21 (1) 5 x 2 y 3 (2) Multiply (1) by 2 and (2) by 34 x 6 y 42 15 x 6 y 9 11x = 33 2 3 3 y 21 x = 3 3 y 27y9 11. Simultaneous Equations1) Eliminate a variable2) Solve for the other variable3) Substitute to find the eliminated variablee.g. (i ) 2 x 3 y 21 (1) 5 x 2 y 3 (2) Multiply (1) by 2 and (2) by 34 x 6 y 42 15 x 6 y 9 11x = 33 2 3 3 y 21 x = 33 y 27 y9 x 3, y 9 12. (ii ) 2 x y 14 (1) x 2 y 2 9 (2) 13. (ii ) 2 x y 14 (1) x 2 y 2 9 (2)Make y the subject in (1)y 14 2 x 14. (ii ) 2 x y 14 (1) x 2 y 2 9 (2)Make y the subject in (1)y 14 2 xSubstitute into (2)x 2 14 2 x 92 15. (ii ) 2 x y 14 (1) x 2 y 2 9 (2) Make y the subject in (1) y 14 2 x Substitute into (2) x 2 14 2 x 92x 2 196 56 x 4 x 2 9 3 x 2 56 x 205 0 16. (ii ) 2 x y 14 (1) x 2 y 2 9 (2) Make y the subject in (1) y 14 2 x Substitute into (2) x 2 14 2 x 92x 2 196 56 x 4 x 2 9 3 x 2 56 x 205 0 3x 41 x 5 0 41x 5 or x 3 17. (ii ) 2 x y 14 (1)x 2 y 2 9 (2)Make y the subject in (1)y 14 2 xSubstitute into (2)x 2 14 2 x 9 2 x 2 196 56 x 4 x 2 93 x 2 56 x 205 0 3x 41 x 5 041 x 5 or x 3 41 142 5 y 14 or 2 y3 40 y 4 or y 3 18. (ii ) 2 x y 14 (1)x 2 y 2 9 (2)Make y the subject in (1)y 14 2 xSubstitute into (2)x 2 14 2 x 9 2 x 2 196 56 x 4 x 2 93 x 2 56 x 205 0 3x 41 x 5 041 x 5 or x 3 41 142 5 y 14 or 2 y3 41 40 40 x 5, y 4 or x , y y 4 or y 333 19. (iii )x 2 y z 5 (1) 2 x 3 y 4 z 28 (2) any time you have the same number ofpronumerals as equations it should 4 x 5 y 3 z 10 (3) be possible to find their values 20. (iii )x 2 y z 5 (1) any time you have the same number of 2 x 3 y 4 z 28 (2) pronumerals as equations it should 4 x 5 y 3 z 10 (3)be possible to find their valuesCreate two pairs of two equations andeliminate the same variable from both 21. (iii )x 2 y z 5 (1) any time you have the same number of 2 x 3 y 4 z 28 (2) pronumerals as equations it should 4 x 5 y 3 z 10 (3)be possible to find their valuesCreate two pairs of two equations andeliminate the same variable from both Multiply (1) by 2 2 x 4 y 2 z 10 2 x 3 y 4 z 28 22. (iii )x 2 y z 5 (1) any time you have the same number of 2 x 3 y 4 z 28 (2) pronumerals as equations it should 4 x 5 y 3 z 10 (3)be possible to find their valuesCreate two pairs of two equations andeliminate the same variable from both Multiply (1) by 2 2 x 4 y 2 z 10 2 x 3 y 4 z 287 y 6 z 38 23. (iii )x 2 y z 5 (1) any time you have the same number of 2 x 3 y 4 z 28 (2) pronumerals as equations it should 4 x 5 y 3 z 10 (3)be possible to find their valuesCreate two pairs of two equations andeliminate the same variable from both Multiply (1) by 2Multiply (1) by 4 2 x 4 y 2 z 104 x 8 y 4 z 20 2 x 3 y 4 z 28 4 x 5 y 3 z 107 y 6 z 38 24. (iii )x 2 y z 5 (1) any time you have the same number of 2 x 3 y 4 z 28 (2) pronumerals as equations it should 4 x 5 y 3 z 10 (3)be possible to find their valuesCreate two pairs of two equations andeliminate the same variable from both Multiply (1) by 2Multiply (1) by 4 2 x 4 y 2 z 104 x 8 y 4 z 20 2 x 3 y 4 z 28 4 x 5 y 3 z 107 y 6 z 38 3 y z 10 25. (iii )x 2 y z 5 (1) any time you have the same number of 2 x 3 y 4 z 28 (2) pronumerals as equations it should 4 x 5 y 3 z 10 (3)be possible to find their valuesCreate two pairs of two equations andeliminate the same variable from both Multiply (1) by 2Multiply (1) by 4 2 x 4 y 2 z 104 x 8 y 4 z 20 2 x 3 y 4 z 28 4 x 5 y 3 z 107 y 6 z 38 3 y z 10Solve these new equations simultaneously 26. (iii )x 2 y z 5 (1) any time you have the same number of 2 x 3 y 4 z 28 (2) pronumerals as equations it should 4 x 5 y 3 z 10 (3)be possible to find their valuesCreate two pairs of two equations andeliminate the same variable from both Multiply (1) by 2 Multiply (1) by 4 2 x 4 y 2 z 104 x 8 y 4 z 20 2 x 3 y 4 z 28 4 x 5 y 3 z 107 y 6 z 38 3 y z 10Solve these new equations simultaneously 7 y 6 z 3818 y 6 z 60 27. (iii )x 2 y z 5 (1) any time you have the same number of 2 x 3 y 4 z 28 (2) pronumerals as equations it should 4 x 5 y 3 z 10 (3)be possible to find their valuesCreate two pairs of two equations andeliminate the same variable from both Multiply (1) by 2 Multiply (1) by 4 2 x 4 y 2 z 104 x 8 y 4 z 20 2 x 3 y 4 z 28 4 x 5 y 3 z 107 y 6 z 38 3 y z 10Solve these new equations simultaneously 7 y 6 z 3818 y 6 z 60 28. (iii )x 2 y z 5 (1) any time you have the same number of 2 x 3 y 4 z 28 (2) pronumerals as equations it should 4 x 5 y 3 z 10 (3)be possible to find their valuesCreate two pairs of two equations andeliminate the same variable from both Multiply (1) by 2Multiply (1) by 4 2 x 4 y 2 z 104 x 8 y 4 z 20 2 x 3 y 4 z 28 4 x 5 y 3 z 107 y 6 z 38 3 y z 10Solve these new equations simultaneously 7 y 6 z 3818 y 6 z 6011 y 22 y 2 29. 3 2 z 10 z 4z4 30. 3 2 z 10 x 2 2 4 5 z 4x3z4 31. 3 2 z 10 x 2 2 4 5 z 4x3z4 x 3, y 2, z 4 32. 3 2 z 10 x 2 2 4 5 z 4x3z4 x 3, y 2, z 4 Exercise 1H; 1bg, 2cfil, 3aceg, 4aegh, 5a, 6ace, 7ad, 8*b, 9***</p>