[table][tr][td]Subject [/td][td]  : Mathematics[br][/td][/tr][tr][td]Class[/td][td]  : VIII SMP[/td][/tr][tr][td]Material[/td][td]  : SYSTEM OF LINEAR EQUATION OF TWO VARIABLES[br][/td][/tr][/table]

[b][color=#0000ff]Basic Competencies:[/color][/b][br][br]3.5 Describe a system of linear equations of two variables and their solutions associated with contextual problems[br]4.5 Solve problems related to systems of linear equations of two variables[br][br][color=#0000ff][b]IPK:[br][/b][/color]3.5.1 Identifying linear equations of two variables [br]3.5.2 Determining the solution set of a two-variable linear equation system using the graph method[br][br][b][color=#0000ff]Learning Objectives:[/color][/b][br]1. Students are able to apply the concept of a two-variable linear equation[br]2. Students are able to solve problems related to a system of linear equations of two variables[br]3. Students are able to solve a system of linear equations of two variables using the graphical method

[b][color=#0000ff]Worksheet Instruction[/color][/b][br]1. Please pray first![br]2. Read the material to remind you again![br]3. Read this student worksheet carefully and answer each question properly and correctly![br]4. The time allotted to do this worksheet is 2x40 minutes![br]5. If something is not clear, ask the teacher![br]6. Summarize what you get from this student worksheet!

[b][size=150][color=#0000ff]A. Variables, Coefficients, and Constants.[br][/color][/size][/b][br]Before studying the System of Linear Equation of Two Variables we must first know what is meant by Variables, Coefficients, and Constants. [br][br]Variable is a example/substitute of a value or number which is usually denoted by a letter/symbol.[br][br]Coefficient is a number that expresses the number of similar variables. Coefficients can also be said to be a number in front of a variable.[br][br]Constant is a number that is not followed by a variable so that its value remains (constant) for any value of the variable (variable).[br][br]Example: [br][math]3x+2y=5[/math][br]Variable  = x and y[br]Coefficient  = 3 and 2[br]Constant  = 5

[b][size=150][color=#0000ff]B. Definition of Linear Equation of Two Variables[/color][/size][/b][br][br]Linear Equation of Two Variables is an equation that contains two variables where the power/degree of each variable is equal to one.[br][br]General Form:[br] Equation 1: ax + by = c[br] Equation 2: px + qy = r[br][br]where x , y is called the variable[br]a, b, p, and q are called coefficients[br]c and r are called the constant

There are so many problems in everyday life that can be solved by using a two-variable linear equation system (SPLDV). Usually these problems are presented in the form of story questions.[br][br]To solving story problems we can use system of linear equations of two variables by change the sentences in the story problems into several mathematical sentences (mathematical models), so as to form a system of linear equations of two variables; [br][br]Example:[br]Asep buys 2 kg of mangoes and 1 kg of apples and he has to pay Rp. 15,000.00, while Intan buys 1 kg of mangoes and 2 kg of apples for Rp. 18,000.00. How much is 5 kg of mango and 3 kg of apples?[br]Please change the above statement to system of linear equations of two variables[br][br]Solution:[br][br]The first step, we have to do is replace all the quantities in the problem with variables.[br]We assume,[br]the price of 1 kg of mango = x, and [br]the price of 1 kg of apples = y[br][br]Then, we make a mathematical model of the problem.[br]2 kg of mangoes and 1 kg of apples and he has to pay Rp. 15,000.00 [math]\Longrightarrow2x+y=15.000[/math][br]1 kg of mangoes and 2 kg of apples for Rp. 18,000.00 [math]\Longrightarrow x+2y=18.000[/math][br][br]Thus, the mathematical model is obtained as follows:[br]Equation 1 : [math]2x+y=15.000[/math][br]Equation 2 : [math]x+2y=18.000[/math][br]

[b][color=#0000ff][size=150]C. Solve SPLDV With Graph Method[/size][/color][/b][br] [br]It has already been mentioned that another way to determine the solution to a two-variable system of linear equations is to use the graphical method.[br] It is known that the graph of the equations of ax+by=c and px+qy=r is described as follows

The points that lie on the line ax + by = c are the solutions to the system of linear equations ax + by = c. Likewise the points that lie on the line px + qy = r. Then which points are the solutions to the system of linear equations ax + by = c and px + qy = r? Of course the points are the solutions to both equations. In this case, it is the point where the two lines intersect, which is A(X[sub]0[/sub],Y[sub]0[/sub]). Thus it can be concluded that:[br]In the graphical method, the solution to a two-variable system of linear equations is the point where the lines of the linear equations intersect.

[b]The steps for solving using the graphical method are as follows:[/b][br]1. Draw the line graphs ax + by = c and px + qy = r on a Cartesian coordinate system. In this step, we must determine the point of intersection of the X axis and the point of intersection of the Y axis, namely the point of intersection of the X axis when y = 0 and the point of intersection of the Y axis when x = 0. Then, the relationship between the two points of intersection is obtained so that the equation line is obtained.[br][br]2. Determine the coordinates of the intersection of the two lines ax + by = c and px + qy = r (if any).[br][br]3. Write down the solution set

EXAMPLE:[br][br]Determine the solution set of the two-variable system of linear equations[br]3x + 4y = 12[br]2x + 4y = 8

So, from this graph we can find the intersect point is (4,0)

Determine the solution set for the following system of linear equations using the graphical method[br]2x + 3y = 12[br]-x + y = -1

EXAMPLE 3

Determine the solution set of the following linear equation of two variables below[br][img]data:image/png;base64,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[/img][br][img]data:image/png;base64,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[/img]

[size=150][b][color=#0000ff]D. Learning Video[br][/color][/b][/size][br]Here we provide a learning video as a reinforcement of the material for a two-variable linear equation system using the graphical method

[b][size=200][size=150][color=#0000ff]EXERCISE[/color][/size][/size][/b]

2. Determine the solution set for the following system of linear equations using the graphical method[br][br][math]2x-7y=17[/math][br][math]4x-5y=25[/math][br]

3. Determine the solution set of the following linear equation of two variables below[br][br][math]7x+3y=-5[/math][br][math]5x+2y=1[/math][br]