[list=1][*]Students are able to determine a two-variable linear equation.[/*][*]Students are able to determine the solution of a system of two-variable linear equations (SPLDV) using substitution, elimination, and graphing methods with systematic steps.[/*][*]Students are able to compare the solutions of SPLDV using different solving methods.[/*][*]Students are able to summarize or conclude the methods of solving SPLDV, including determining the most appropriate method for a given situation.[/*][/list]
Tissa went to a stationery store. She bought 3 notebooks and 5 pens, paying Rp19,000.00. Determine the two-variable linear equation based on Tissa's situation!
Veronika went to a grocery store. She planned to buy red rice and wheat flour. The price of 1 kg of red rice is Rp20,000.00, while the price of 1 kg of wheat flour is Rp10,000.00. Veronika paid Rp120,000.00. Determine the two-variable linear equation that relates the weight of red rice and wheat flour (in kg) to the total amount paid by Veronika!
Look at the image below![br][img]https://cdn.geogebra.org/resource/euyhvtkj/EXkumuwpcNYMayW5/material-euyhvtkj.png[/img][br]If the price of one bottle of soy milk is represented by [math]x[/math] and the price of one bottle of cow's milk is represented by [math]y[/math], determine the two-variable linear equation based on the information in the image above.
The perimeter of an isosceles triangle is given as 48 cm. Determine the two-variable linear equation that relates the perimeter and the side lengths of the triangle.
[b]Media Usage Instructions[/b][list=1][*]Determine two two-variable linear equations to be entered into the media.[/*][*]Enter the coefficients and constants for each given two-variable linear equation. For equation 1, input the values in the [math]a_1x+b_1y=c_1[/math] column, and for equation 2, input the values in the [math]a_2x+b_2y=c_2[/math] column.[/*][*]Once all values are entered, the system of two-variable linear equations you provided will be displayed on the yellow board.[/*][*]Solve steps 1 to 3 based on the substitution method procedure above. Input values in each white-colored column to find the values of [math]x[/math] and [math]y[/math].[/*][*]Click the 'Check Answer' button to verify whether your answer is correct or incorrect.[/*][*][b][i]HAPPY WORKING! :)[/i][/b][/*][/list]
[b]Use the Learning Media Above to Solve the Following Problem.[/b]
Observe Mr. Ahmad's problem below to answer the following question. Then, help Mr. Ahmad solve the problem.[br][img]https://cdn.geogebra.org/resource/k2wz67sn/9WUsJ0C0o8P3ti7u/material-k2wz67sn.png[/img][br]Which of the following represents the value of [math]x[/math] (indicating the number of mountain bikes) and [math]y[/math] (indicating the number of racing bikes) in Mr. Ahmad's case? [br](Clue: Simplify the two-variable linear equation that can be simplified!)
[math]-x+3y=-5[/math][br][math]2x-5y=8[/math][br]The solution set of the system of two-variable linear equations (SPLDV) above is...
Observe the image of a ping pong ball being launched from a slingshot below.[br][img]https://cdn.geogebra.org/resource/uh9vqry7/X7yIWX8VN3dS3HEO/material-uh9vqry7.png[/img][br]A ping pong ball is launched from a slingshot. When moving against the wind, its speed is 6 m/s, while when moving with the wind, its speed becomes 10 m/s. If [math]x[/math] represents the speed of the ping pong ball without the influence of wind and [math]y[/math] represents the wind speed, determine the values of [math]x[/math] and [math]y[/math] by solving the system of equations:[br][center][math]x-y=6[/math][br][math]x+y=10[/math][/center]
[b]Media Usage Instructions[/b][list=1][*]Determine two two-variable linear equations to be entered into the media.[/*][*]Enter the coefficients and constants for each given two-variable linear equation. For equation 1, input the values in the [math]a_1x+b_1y=c_1[/math]column, and for equation 2, input the values in the [math]a_2x+b_2y=c_2[/math] column.[/*][*]Once all values are entered, the system of two-variable linear equations you provided will be displayed on the purple board.[/*][*]Observe each step of the solution provided in the media.[/*][*][b][i]HAPPY WORKING! :)[/i][/b][/*][/list]
[b]Use the Learning Media Above to Solve the Following Problem.[/b]
Create a system of two-variable linear equations (SPLDV) with the following coefficients [math]a[/math] and [math]b[/math].[br][center][math]ax+4y=8[/math][br][math]3x+by=12[/math][/center]Determine the values of [math]a[/math] and [math]b[/math] so that the system has a solution of [math]x=2[/math] dan [math]y=1[/math]!
[math]a=2[/math] dan [math]b=6[/math]
Determine the solution set of the following system of two-variable linear equations:[br][center][math]-3x+2y=12[/math][br][math]5x-4y=-6[/math][/center]Verify whether the values of [math]x[/math] and [math]y[/math] are:[br][list=1][*]Integers[/*][*]Whole numbers[/*][/list][list][/list]
[list=1][*]The integer solution that satisfies the system of two-variable linear equations (SPLDV) is [math]x=-18[/math] dan [math]y=-21[/math].[/*][*]The solution for whole numbers does not exist.[/*][/list]
Create a system of two-variable linear equations (SPLDV) that has a unique solution of [math]x=-1[/math] dan [math]y=4[/math].
[math]2x+3y=10[/math][br][math]5x-y=-9[/math]
[b]Media Usage Instructions[/b][list=1][*]Determine two two-variable linear equations to be entered into the media.[/*][*]Enter the coefficients and constants for each given two-variable linear equation. For Equation 1, input the values in the [math]a_1x+b_1y=c_1[/math] column, and for Equation 2, input the values in the [math]a_2x+b_2y=c_2[/math] column.[/*][*]Determine the [math]x[/math]-intercept and [math]y[/math]-intercept for both Equation 1 and Equation 2, then input these values into the cream-colored columns in the blue table.[/*][*]Pay attention to the 'Correct' or 'Incorrect' indicators that appear when you input the intercepts.[/*][*]Each equation will generate Points A and B (for Equation 1) and Points C and D (for Equation 2).[/*][*]Click the 'Point A', 'Point B', and corresponding buttons to display the intercepts on the graph.[/*][*]Click the 'Graph 1' button to display the graph of Equation 1. Do the same for 'Graph 2'.[/*][*]You can now observe the intersection of Equation 1 and Equation 2.[/*][*]Click the 'Solution Set' (HP) button to display the solution set of both equations.[/*][*]Click the 'Delete' button if you need to restart the process.[/*][*][b][i]HAPPY WORKING! :)[/i][/b][/*][/list]
Using the graphing method, determine the solution of the following system of linear equations.[br][center][math]6x+5y=9[/math][br][math]2x-3y=3[/math][/center]
Determine the solution of the following system of linear equations.[br][center][math]2x+y=4[/math][br][math]x-y=-1[/math][/center]
Joko is solving the following system of two-variable linear equations:[br][center][math]x+2y=10[/math][br][math]-2x+3y=-6[/math][/center]What are the values of [math]x[/math] and [math]y[/math] that Joko must find as the solution to the system of equations above?
[b]After solving the SPLDV problems above using various solution methods, answer the following questions based on your experience![/b]
How much time did you need to solve the problem using each method?
Which method do you find the easiest and most enjoyable?
In what situations is the substitution method more useful?
In what situations is the elimination method more useful?
In what situations is the graphic method more useful?
After learning about the System of Two-Variable Linear Equations (SPLDV), write your conclusions!
Mention 3 benefits of studying SPLDV based on your experience in the various activities above!
How did the GeoGebra-based worksheet help you understand the concept of SPLDV?
