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Transcript
In this chapter, you will learn to: Solve simultaneous linear equations by the elimination method Solve simultaneous linear equations by the substitution method Express problems in the form of simultaneous linear equations and solve them Solving Simultaneous Linear Equations by the Elimination Method Example 1 Solve the simultaneous equations: 4x – 5y = 17, x – 5y = 8. Solution 4x – 5y = 17 ----- (1) x – 5y = 8 ----- (2) (1) - (2): We eliminate y as the numerical value of the coefficient of y is the same. We subtract equation (2) from (1) as the signs are the same 3x = 9 x=3 Substitute x = 3 into (1): 4(3) - 5y = 17 -5y = 5 y = -1 Note: x = 3 can be substituted into equation (1) or (2) to obtain the value of y x = 3, y = -1. Example 2 Solve the simultaneous equations: 3x + 2y = 8, 4x – y = 7. Solution 3x + 2y = 8 4x – y = 7 ----- (1) ----- (2) (2) × 2: 8x - 2y = 14 ----- (3) (1) + (3): 11x = 22 x=2 Substitute x = 2 into (2): 4(2) - y = 7 8-y=7 y=1 x = 2, y = 1. Multiply (2) by 2 to make the coefficients of y in both equations numerically equal Example 3 Solve the simultaneous equations: 2x + 3y = 12, 5x – 2y = 11. Solution 2x + 3y = 12 ----- (1) 5x – 2y = 11 ----- (2) (1) × 2: (2) × 3: 4x + 6y = 24 ----- (3) 15x – 6y = 33 ----- (4) (3) + (4): 19x = 57 x=3 Substitute x = 3 into (1): 2(3) + 3y = 12 3y = 6 y=2 x = 3, y = 2. The coefficients of y in both equations will be numerically equal if we multiply (1) by 2 and (2) by 3 Note: In the process of solving simultaneous linear equations, either one of the unknowns may be eliminated first Page Homework Use the elimination method to solve the following simultaneous equations. 1. 8x + 13y = 2 5x + 13y = 11 2. 11x + 4y = 12 9x - 4y = 8 3. 7x – 3y = 15 11x – 3y = 21 4. 5x + 7y – 17 = 0 7y + 3x – 27 = 0 5. 4x – 3y = 31 16x + 5y = 39 6. 6x + 5y = 10.5 5x – 3y = -2 7. 4(2x – y + 3) = 0 2(x + y) – 3(x - y) = 6 2 Practice Questions Use the elimination method to solve the following simultaneous equations. 1. 11x + 3y = -10 11x + 7y = 6 2. 13x + 9y = 4 17x - 9y = 26 3. 5x - 6y = 14 5x - 5y = 15 4. 3y – 2x +15 = 0 2x – 2y + 19 = 0 5. 7h – 2k = 17 3h + 4k = 17 6. 10x – 3y = 24.5 3x – 5y = 13.5 7. (x + y)/5 = (x - y)/7 3x + 17y = 2