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Understanding Solutions of Linear Equations with Two Variables

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This lesson explores how to find solutions to equations with two variables through real-world scenarios, such as Mary’s cupcake purchase for her birthday party. It introduces the equation x + y = 10, representing the total cupcakes needed. Students will learn to create ordered pairs as solutions, graph the equations, and use inequalities to examine possible purchase combinations. By completing tables and graphing various linear equations, learners will deepen their understanding of linear relationships between variables.

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Understanding Solutions of Linear Equations with Two Variables

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  1. Equations with two variables I can find solutions of equations with two variables and graph the equation.

  2. Mary is buying pink and blue cupcakes for her birthday party. She needs a total of 10 cupcakes. How many of each type could she get? If x represents pink and y represents blue, what equations could we use to represent the situation? x + y = 10

  3. X + Y = 10 • Complete the table to show the possible answers. Pink (x) Blue (y) • When Mary changes the number of pink cupcakes she buys, the number of blue changes also. Both quantities vary so there are two variables. • When the values in an ordered pair make an equation with two variables true, the ordered pair is a solution.

  4. Pink (x) Blue (y) Give three solutions to the problem. Write them as ordered pairs. (x,y) 1. (0,10) (1,9) (8,2) Graph the solutions

  5. Tell whether each ordered pair is a solution of the equation. y = -7x + 10; (-3, 31), (7, 59), (0, 10)

  6. Use the inequality y = 2x – 4. Complete each solution. • (0, ?) • (50, ?) • (-17, ?)

  7. The equation y = 3x + 12 describes the cost y to rent x videos. Complete the solution (8, ?) How much will it cost to rent 8 videos?

  8. Graph y = 3x + 4

  9. Graph y = -3x - 5

  10. Graph y = 3/4x - 1

  11. Summarize Explain how to graph the equation y = x + 2.

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