with a1, a2, b1, b2, c1, and c2 are real numbers.
To determine the set of linear equations system solving is to find the price of variables that satisfy the system of equations. Settlement set can be searched by using:
- The method of elimination
- Substitution
- or a mixture of both methods.
1. Elimination Method
Elimination means to wipe out. Complete the system of linear equations of two variables by means of elimination which means finding the value of the variable by eliminating other variables by subtracting or summing them up.To eliminate that variable, the coefficient should be the same. If not the same then each equation is multiplied by a certain number so it has the same coefficient.
If one of two variables has the same coefficient, then the equation of one is added to the other. But if it has the opposite coefficient, the one equation is subtracted by the other.
Example:
Specify the set of completions from:
To find the variable y means the x is eliminated. To eliminate or eliminate the variable x, then the coefficient x is first equated by multiplying with a number such that the coefficients of the two equations are the same.
Now eliminate the y variable to find x
The set of solutions for such a system of linear equations is {(1, 2)}
2. Substitution Method
Substitution means changing or declaring one variable with another variable.Example:
Specify the set of completions from:
Answer:
Suppose that to be substituted or replaced is a variable in equation 2), then equation 1) is expressed in the form y = 5 - 3x.
Then, x = 3 is substituted to y = 5 - 3x
y = 5 - 3x
y = 5 - 3(3)
y = 5 - 9
y = -4
So the set of settlements is {(3, -4)}
3. Mixed Methods
The mixed method is a combination of elimination and substitution methods.Example:
Specify the set of completions from:
Answer:
Becouse the coefficients of x are the same, the eliminated variable is x by subtracting it.
Substitute y = 1 to one of the equations to get the x variable.
So the set of solutions is {(0, 1)}
Similarly this article.
Sorry if there is a wrong word.
The end of word wassalamualaikum wr. wb
Referensi :
- To'Ali's book math group accounting and sales
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