SOLVING SIMULTANEOUS EQUATION : Solving by Elimination Method

How to solve - Solving Simultaneous Equation : Solving by Elimination Method?
- Group the equations into first (1) and second (2) equations.
- Two equations are simplified by adding or subtracting them.
- This eliminates one of the variables so that the other variable can be found.
- Find the other variable by substituting the first variable to either the two original equations
Examples : Solving Simultaneous Equation by Elimination method.
EXAMPLE 17a−2b=266a+5b=29 |
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Step (1) Group the equations into first (1) and second (2) equations. | 7a−2b=26→(1)6a+5b=29→(2) |
Step (2) Two equations are simplified by adding or subtracting them. Step (3) This eliminates one of the variables so that the other variable can be found. |
(1)×6 42a−12b=156→(3)(2)×7 42a+35b=203→(4)(3)−(4) |42a42a||−12b+35b|==|156203| |−12b−35b|=|156−203| −47b=−47b=1 |
Step (4) Find the other variable by substituting the first variable to either the two original equations | Substitute b = 1 into (1) 7a−2(1)=267a=26+27a=28a=287a=4 |
EXAMPLE 2x+2y=−14x−3y=18 |
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Step (1) Group the equations into first (1) and second (2) equations. | x+2y=−1→(1)4x−3y=18→(2) |
Step (2) Two equations are simplified by adding or subtracting them. Step (3) This eliminates one of the variables so that the other variable can be found. |
(1)×4 4x+8y=−4→(3)4x−3y=18→(2)(3)−(2) |4x4x||+8y−3y|==|−418||8y−3y|=|−4−18| 11y=−22y=−2211y=−2 |
Step (4) Find the other variable by substituting the first variable to either the two original equations | x+2(−2)=−1x−4=−1x=−1+4x=3 |
Try it yourself - Solving Simultaneous Equation by Elimination method
x+y=7x−y=3 | x=5,y=2 |
2x+5y=7x+3y=4 | x=1,y=1 |
3x+2y=124x−y=5 | x=2,y=3 |
5x−3y=113x+y=8 | x=2.5,y=0.5 |
5x=2y3x+7y=41 | x=−2.83,y=−7.07 |
3x−2y=132x+5y=−4 | x=3,y=−2 |
5x=1−3y2x+y+4=0 | x=−13,y=22 |
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