SPLDV

2-VARIABLE LINEAR EQUATION SYSTEM (SPLDV)

Definition of SPLDV

SPLDV is a….

system of equations or forms of relationships similar to in the form of algebra  which has two variables and one rank and if depicted in a graph it will form a   straight line. And because of this, this equation is called a linear equation.

Characteristics of SPLDV

Ø  Use the equal sign relation (=)

Ø  Has two variables

Ø  Both of these variables have first degree (pangkat satu)

          

Matters relating to SPLDV

A. Tribe

Tribe is a part of an algebraic form consisting of variables, coefficients and constants.     And each tribe is separated by addition or subtraction punctuation

Example:

6x - y + 4, then the tribes of the equation are 6x, -y and 4

B. Coefficient

Coefficient is a number that states the number of a number of similar variables. The coefficient is also called the number that is in front of the variable, because the writing of a coef fi cient equation is in front of the variable.

           Example:

Mika has 2 pineapple and 5 oranges. If written in the form of equations are:

Answer:

    Pineapple = x and Orange = y

    The connection is 2x + 5y

    Where 2 and 5 are coefficients. And 2 is the coefficient x and 5 is the coefficient y

 C. Variable

Variables, namely variables or substitutes for a number that is usually denoted by letters such as x and y.

Example:

Mika has 2 pineapple and 5 oranges.

If written in the form of an equation is

Pineapple = x

Orange = y

The connection is 2x + 5y

D. Constant

Constants are numbers that are not followed by variables, the value is constant or constant for whatever the value of the change is

Example:

2x + 5y + 7, from the equation the constant is 7, because 7 values ​​are fixed and are not affected by any variable.

Method of Completion of Two Variable Linear Equation Systems

 To complete the spldv calculation method (a linear two-variable system of equations) it can be solved with the following 4 methods:

1. Substitution Method

2. Elimination Method

3. Combined Method (Substitution and Elimination)

4. Graph Method

Following are the steps to complete  spldv using the Substitution method

1. Change one of the equations to the form x = cy + d or y = ax + b
   - a, b, c, and d are the values in the equation
   - The trick is you have to look for two equations,find one of the easiest equations.

2. After getting the equation, substitute the x or y value
3. Complete the equation so that you get the value x or   y
4. Get the value of the variable that is not yet known with the results of the previous step.

Look for the following resolution sets for each SPLDV.
5x + 5y = 25
3x + 6y = 24
Answer
5x + 5y = 25 ………. Pers. (1)
3x + 6y = 24 ………. Pers. (2)
From equation (1) we get the y equation as follows.
⇔ 5x + 5y = 25
⇔ 5y = 25 - 5x
⇔ y = 5-x
Then we substitute the y equation to equation (2) as follows.
⇔ 3x + 6 (5 - x) = 24
⇔ 3x + 30 - 6x = 24
⇔ 30 - 3x = 24
⇔ 3x = 30-24
⇔ 3x = 6
⇔ x = 2
Finally, to determine the y value, we substitute the value of x to equation (1) or equation (2) as follows.
⇔ 5 (2) + 5y = 25
⇔ 10 + 5y = 25
⇔ 5y = 25-10
⇔ 5y = 15
⇔ y = 3
So, the set of resolutions from the SPLDV is {(2, 3)}.

steps to complete spldv with the elimination method:    

1. Elimination method is a method or way to solve a    system of linear equations in two variables by           eliminating or eliminating one variable (variable) by  equating the coefficient of the equation.
2. The way to eliminate one of the variables is by        observing the sign, if the sign is the same as [(+)      with (+) or (-) with (-)], then to eliminate it by          subtracting it. And vice versa if the mark is different   then use the addition system.

                                                                                        

Determine the set of resolutions of the equation x + 3y = 15 and

3x + 6y = 30
Known :
Equation 1 = x + 3y = 15
Equation 2 = 3x + 6y = 30

The first step is to determine which variables will be eliminated first.

This time we will remove x first, and so we find the y value. The          methods are:

3x + 6y = 30 : 3
x + 2y = 10. . . . (1)
x + 3y = 15. . . (2)

The Second Step From equations (1) and (2), let's eliminate, so the        result:
x + 3y = 15
x + 2y = 10 _
y = 5

Third Step Next, to find out the value of x, then the way is as       follows:

x + 3y = 15 | x2 | <=> 2x + 6y = 30. . . (3)
3x + 6y = 30 | x1 | <=> 3x + 6y = 30. . ... (4)

The elimination between equations (3) with (4), the result being:

3x + 6y = 30
2x + 6y = 30 _
x = 0

Then, the solution is HP = {0. 5}

https://rumusrumus.com/spldv/

https://rumushitung.com/2015/10/31/spldv-matematika-smp/