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

1. Elimination / Addition
●
We eliminate one of the unknowns by adding or
subtracting the equations.

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. Elimination / Addition
For example:
3x−2y=1
x4y=19
}

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. 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. 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. Elimination / Addition
The same example, now eliminating the ”y”.
3x−2y=1
x4y=19
}

8. Elimination / Addition
The same example, now eliminating the ”y”.
3x−2y=1
x4y=19
}
6x−4y=2
⇒
x4y=19
}

9. Elimination / Addition
We add the equations:
6x−4y=2
x4y=19
7x=21
21
x=
7
x=3
}

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