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# Elimination

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Elimination (also called addition9 method to resolve a system of linear equations

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### Elimination

1. 1. Elimination / Addition ● We eliminate one of the unknowns by adding or subtracting the equations.
2. 2. Elimination / Addition We eliminate one of the unknowns by adding or subtracting the equations. ● To do so, sometimes we must multiply one or both equations by certain numbers until we have the same unknown with opposite coefficients. ●
3. 3. Elimination / Addition For example: 3x−2y=1 x4y=19 }
4. 4. Elimination / Addition To get rid of the ”x”, I have to multiply the second equation by –3. } 3x−2y=1   ⇒   3x−2y=1 x4y=19 −3x−12y=−57 }
5. 5. Elimination / Addition We add now both sides of the equations separatedly: 3x−2y=1 −3x−12y=−57 } −14y=−56 −56 y= −14 y=4
6. 6. Elimination / Addition All that rests now is finding the value of x, plugging the value y=4 in either of the equations: x4y=19   ⇒   x4 ∙ 4=19 x=19−16 x=3
7. 7. Elimination / Addition The same example, now eliminating the ”y”. 3x−2y=1 x4y=19 }
8. 8. Elimination / Addition The same example, now eliminating the ”y”. 3x−2y=1 x4y=19 } 6x−4y=2  ⇒  x4y=19 }
9. 9. Elimination / Addition We add the equations: 6x−4y=2 x4y=19 7x=21 21 x= 7 x=3 }
10. 10. Elimination / Addition Now we just have to plug the value x=3 in either of the equations: x4y=19   ⇒   34y=19 4y=19−3 16 y= 4 y=4