Linear Equations in Two Variables
21 likes23,143 views
The document discusses linear equations in two variables. It defines a linear equation as one that can be written in the standard form Ax + By = C, where A, B, and C are real numbers and A and B cannot both be zero. Examples are provided of determining if equations are linear and identifying the A, B, and C components if they are linear. The document also discusses using ordered pairs as solutions to linear equations and finding multiple solutions to a given linear equation.
Linear Equations in Two Variables
- 1. Linear Equation in Two Variables Prepared by: Ms. Ma. Irene G. Gonzales
- 2. Lesson Objectives: At the end of the period, students should be able to: • illustrate linear equations in two variables; • determine if an ordered pair is a solution of a given linear equation; and • graph linear equations in two variables;
- 3. Linear Equation in Two Variables An equation that can be written in the standard form Ax + By = C where A, B and C are real numbers but A and B cannot both be zero. Learning Objective: Students should be able to illustrate linear equations in two variables.
- 4. Determine whether or not each equation is a linear equation in two variables. If so, identify A, B and C. 5x = 10 + 3y is a linear equation in two variables A = 5 B = -3 C = 10 5x = 10 + 3y 5x - 3y = 10 + 3y - 3y 5x – 3y = 10 Learning Objective: Students should be able to illustrate linear equations in two variables.
- 5. Determine whether or not each equation is a linear equation in two variables. If so, identify A, B and C. y = 4x + 9 is a linear equation in two variables A = 4 B = -1 C = -9 y = 4x + 9 y – 4x = 4x – 4x + 9 - 4x + y = 9 4x – y = -9 Learning Objective: Students should be able to illustrate linear equations in two variables.
- 6. Determine whether or not each equation is a linear equation in two variables. If so, identify A, B and C. This is not a linear equation because the exponent of x is 2. 3x2 – y = 9 Learning Objective: Students should be able to illustrate linear equations in two variables.
- 7. Determine whether or not each equation is a linear equation in two variables. If so, identify A, B and C. This is not a linear equation because a variable appears in the denominator of a fraction. 20 3 y x Learning Objective: Students should be able to illustrate linear equations in two variables.
- 8. Determine whether or not each equation is a linear equation in two variables. If so, identify A, B and C. This is not a linear equation because the two variables are part of the same term. 15xy Learning Objective: Students should be able to illustrate linear equations in two variables.
- 9. Determine whether or not each equation is a linear equation in two variables. If so, identify A, B and C. x = 8 – 3y is a linear equation in two variables A = 1 B = 3 C = 8 x = 8 – 3y x + 3y = 8 – 3y + 3y x + 3y = 8 Learning Objective: Students should be able to illustrate linear equations in two variables.
- 10. Solutions of a Linear Equation in Two Variables These are ordered pairs (x, y) that make the equation true. Example 1: Is the ordered pair (2, 2) a solution of x + 3y = 8? How about (-1, 3)? (-2, -2)? Learning Objective: Students should be able to determine if an ordered pair is a solution to a linear equation.
- 11. Determine if the given ordered pair is a solution of x + 4y = 7. a. (3, 1) b. (-1, 2) c. (2, -1) Learning Objective: Students should be able to determine if an ordered pair is a solution to a linear equation.
- 12. The question is…
- 13. Challenge Accepted!!! Find three solutions of 4x + y = 12. Solution: We find three ordered pairs that satisfy the given equation. Learning Objective: Students should be able to determine if an ordered pair is a solution to a linear equation.
- 14. Learning Objective: Students should be able to graph linear equations in two variables.