In the previous material has been studied about the linear equation of two variables, namely the equation that contains two variables with the highest rank of one. The general form is ax + by + c = 0. In this case a and b are each called the coefficients of x and y, while c is called a constant.
The solution of the linear equation of two variables ax + by + c = 0, is a sequential pair (x, y) that satisfies the equation. These sequential pairs, if drawn into a Cartesius graph, are infinite points, forming a straight line.
The system of two-variable linear equations are several linear equations that form a system, so that the solution is the intersection of all the lines of the linear equation.
The method of determining the set of solutions of this system of linear equations is
(1) Graphic method(2) Elimination method
(3) Substitution method In the
following, the explanations of the three methods above will be described.
Graphical Method
. Suppose that a system of linear equations is known:
So the solution is the intersection of the two linear lines. So with the graph method, the two linear equations must be drawn on a Cartesius graph. For more details will be described in the following example:
01. Using the graph method, determine the solution of a system of linear equations 2x + 5y = 20 and x – y = 3
Answer:
With the graph method, it can be known that there are three possible solutions to the system of linear equations, namely:
For more details, follow the following example:
02. Known system of linear equations ax + 2y = 5 and 15x – 5y = 14. Determine the value of a so that the system of linear equations has no solution point
Answer
Substitution Method
The solution of the system of linear equations by the substitution method, is done by “replacing” one variable into another variable.
For more details, follow the following example:
03. Using the substitution method, find the solution of the system of linear equations 3x + y = 3 and 2x – 3y = 13
Answer
3x + y = 3
y = 3 – 3x
substituted to 2x – 3y = 13
obtained: 2x – 3 (3 – 3x) = 13
2x – 9 + 9x = 13
11x = 13 + 9
11x = 22
x = 2
so that y = 3 – 3 (2) = 3 – 6 = –3
So the solution is: {(2, –3)
04. Using the substitution method, find the solution of the system of linear equations 5x – 2y = 1 and 2x + 3y = 8
Answer
Elimination Method
The solution of the system of linear equations with the elimination method, is done by “eliminating” one variable so that the value of another variable is obtained.
For more details, follow the following example:
05. By the elimination method, determine the solution of the system of linear equations 2x – 3y = 2 and 5x + 2y = –14
Answer
06. Using the elimination method, find the solution of the system of linear equations 6x + y = 11 and x + 3y = –1
Answer
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