English adaptation of “Sistemas de Ecuaciones Lineales por Método Gráfico” by Andrés Aguilera Abarca.[br][br]Original GeoGebra resource: https://www.geogebra.org/m/nCdXe4Sz[br][br]Translated and adapted into English by Mario I. Estrada-Delgado.[br][br]Licensed under CC BY-NC-SA 4.0.[br][br][br]Systems of Linear Equations: Graphical Method[br][br]The following applet allows you to solve systems of linear equations using the graphical method.[br][br]Recall that to graph a linear equation in two variables, you can follow the same procedure used for linear functions. Create a table containing at least two points (x, y). Assign a value to x and solve the equation to obtain the corresponding value of y (or vice versa). Plot the points and draw the straight line passing through them.[br][br]Repeat the same procedure for the second linear equation.[br][br]Check your results using the tables: enter the x-values you used and verify that the corresponding y-values are correct.[br][br]Use the applet to find the solutions to the systems of equations provided by your instructor, and then answer the corresponding questions.[br][br]Move the a, b, c, d, e, and f sliders to reproduce the two linear equations of each system.[br][br]The solution of the system of linear equations is the point at which the two lines intersect.[br][br]Tip: Make sure that the equations are written in the same form as the equations shown in the green box. If they are not, use algebraic manipulation to rewrite them in the required form.

From the list of systems of equations provided by your instructor:[br][br]1. Which systems of linear equations have one solution? What do their graphs have in common?[br][br]2. Which systems of linear equations have no solution? What do their graphs have in common?[br][br]3. Which systems of linear equations have infinitely many solutions? What do their graphs have in common?[br][br]Write a conclusion in your notes based on your observations about the graphical solutions of systems of linear equations.