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This document discusses linear equations in two variables. It begins with definitions, stating that a linear equation in two variables is an equation of the form ax + by + c = 0, where a, b, and c are real numbers and a and b are not both zero. It then provides 8 facts about linear equations, such as that their graphs are straight lines and they have infinitely many solutions. It concludes by outlining procedures for finding a solution, finding a solution from a graph, and drawing the graph of a linear equation.
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- 1. In this document you can review important • Definitions • Facts • Procedures Class – IX, CBSE MB0904: Linear Equations in Two variables Learn Math for Free. Visit www.ganitgurooz.com
- 2. What is a Linear Equations in two variables? Class – IX,CBSE MB0904: Linear Equations in Two variables Important Definitions Topic: Linear Equations Learn Math for Free. Visit www.ganitgurooz.com
- 3. What is a Linear Equations in two variables? Class – IX,CBSE Important Definitions An equation of the form ax+by+c = 0, where a, b and are real numbers, such that a and b are not both zero, is called a linear equation in two variables. c Learn Math for Free. Visit www.ganitgurooz.com MB0904: Linear Equations in Two variables Topic: Linear Equations
- 4. Fact # 1 A linear equation in two variables has infinitely many solutions. Class – IX,CBSE Important Facts Learn Math for Free. Visit www.ganitgurooz.com MB0904: Linear Equations in Two variables Topic: Linear Equations
- 5. Fact # 2 The graph of every linear equation in two variables is a straight line. Class – IX,CBSE Important Facts Learn Math for Free. Visit www.ganitgurooz.com MB0904: Linear Equations in Two variables Topic: Linear Equations
- 6. Fact # 3 is the equation of the y-axis. Class – IX,CBSE Important Facts Learn Math for Free. Visit www.ganitgurooz.com MB0904: Linear Equations in Two variables 0x Topic: Linear Equations
- 7. Fact # 4 is the equation of the x-axis. Class – IX,CBSE Important Facts Learn Math for Free. Visit www.ganitgurooz.com MB0904: Linear Equations in Two variables 0y Topic: Linear Equations
- 8. Fact # 5 The graph of is a straight line parallel to the y-axis. Class – IX,CBSE Important Facts Learn Math for Free. Visit www.ganitgurooz.com MB0904: Linear Equations in Two variables x a Topic: Linear Equations
- 9. Fact # 6 The graph of is a straight line parallel to the x-axis. Class – IX,CBSE Important Facts Learn Math for Free. Visit www.ganitgurooz.com MB0904: Linear Equations in Two variables y a Topic: Linear Equations
- 10. Fact # 7 An equation of the type represents a line passing through the origin. Class – IX,CBSE Important Facts Learn Math for Free. Visit www.ganitgurooz.com MB0904: Linear Equations in Two variables y mx Topic: Linear Equations
- 11. Fact # 8 Every point on the graph of a linear equation in two variables is a solution of the linear equation. Moreover, every solution of the linear equation is a point on the graph of the linear equation. Class – IX,CBSE Important Facts Learn Math for Free. Visit www.ganitgurooz.com MB0904: Linear Equations in Two variables Topic: Linear Equations
- 12. How to find a solution of a linear equation in 2 variables? Class – IX,CBSE Important Procedures Learn Math for Free. Visit www.ganitgurooz.com MB0904: Linear Equations in Two variables Topic: Solution of a Linear Equation
- 13. How to find a solution of a linear equation in 2 variables? Class – IX,CBSE Important Procedures Learn Math for Free. Visit www.ganitgurooz.com : Assume any value of one of the two variables.Step 1 MB0904: Linear Equations in Two variables Topic: Solution of a Linear Equation
- 14. How to find a solution of a linear equation in 2 variables? Class – IX,CBSE Important Procedures Learn Math for Free. Visit www.ganitgurooz.com : Put this value in the equation to get a linear equation in one variable.Step 2 MB0904: Linear Equations in Two variables : Assume any value of one of the two variables.Step 1 Topic: Solution of a Linear Equation
- 15. How to find a solution of a linear equation in 2 variables? Class – IX,CBSE Important Procedures Learn Math for Free. Visit www.ganitgurooz.com : Solve the equation obtained in step 2 to find the value of the second variable.Step 3 MB0904: Linear Equations in Two variables : Assume any value of one of the two variables.Step 1 : Put this value in the equation to get a linear equation in one variable.Step 2 Topic: Solution of a Linear Equation
- 16. How to find a solution of a linear equation in 2 variables? Class – IX,CBSE Important Procedures Learn Math for Free. Visit www.ganitgurooz.com : The two values (from Step 1 and Step 4) are a solution of the linear equation.Step 4 MB0904: Linear Equations in Two variables : Solve the equation obtained in step 2 to find the value of the second variable.Step 3 : Assume any value of one of the two variables.Step 1 : Put this value in the equation to get a linear equation in one variable.Step 2 Topic: Solution of a Linear Equation
- 17. How to find a solution of a linear equation in 2 variables? Class – IX,CBSE Important Procedures Learn Math for Free. Visit www.ganitgurooz.com MB0904: Linear Equations in Two variables : The two values (from Step 1 and Step 4) are a solution of the linear equation.Step 4 : Solve the equation obtained in step 2 to find the value of the second variable.Step 3 : Assume any value of one of the two variables.Step 1 : Put this value in the equation to get a linear equation in one variable.Step 2 : Note that we always write the -value first when writing the solution as a pair.xStep 5 Topic: Solution of a Linear Equation
- 18. How to find a solution from the graph of a linear equation in 2 variables? Class – IX,CBSE Important Procedures Learn Math for Free. Visit www.ganitgurooz.com MB0904: Linear Equations in Two variables Topic: Solution of a Linear Equation
- 19. How to find a solution from the graph of a linear equation in 2 variables? Class – IX,CBSE Important Procedures Learn Math for Free. Visit www.ganitgurooz.com :Select any point on the line in the graph.Step1 MB0904: Linear Equations in Two variables Topic: Solution of a Linear Equation
- 20. How to find a solution from the graph of a linear equation in 2 variables? Class – IX,CBSE Important Procedures Learn Math for Free. Visit www.ganitgurooz.com MB0904: Linear Equations in Two variables :Select any point on the line in the graph.Step1 :Draw a vertical line from the point to intersect the -axis.xStep2 Topic: Solution of a Linear Equation
- 21. How to finding a solution from the graph of a linear equation in 2 variables? Class – IX,CBSE Important Procedures Learn Math for Free. Visit www.ganitgurooz.com How to find a solution from the graph of a linear equation in 2 variables? :Select any point on the line in the graph.Step1 :Draw a vertical line from the point to intersect the -axis.xStep2 :Note the point where it intersects the -axis.xStep3 MB0904: Linear Equations in Two variables Topic: Solution of a Linear Equation
- 22. How to finding a solution from the graph of a linear equation in 2 variables? Class – IX,CBSE Important Procedures Learn Math for Free. Visit www.ganitgurooz.com MB0904: Linear Equations in Two variables How to find a solution from the graph of a linear equation in 2 variables? :Select any point on the line in the graph.Step1 :Draw a vertical line from the point to intersect the -axis.xStep2 :Note the point where it intersects the -axis.xStep3 :Draw a horizontal line from the point to intersect the -axis.yStep4 Topic: Solution of a Linear Equation
- 23. How to finding a solution from the graph of a linear equation in 2 variables? Class – IX,CBSE Important Procedures Learn Math for Free. Visit www.ganitgurooz.com MB0904: Linear Equations in Two variables How to find a solution from the graph of a linear equation in 2 variables? :Select any point on the line in the graph.Step1 :Draw a vertical line from the point to intersect the -axis.xStep2 :Note the point where it intersects the -axis.xStep3 :Draw a horizontal line from the point to intersect the -axis.yStep4 :Note the point where it intersects the -axis.yStep5 Topic: Solution of a Linear Equation
- 24. How to finding a solution from the graph of a linear equation in 2 variables? Class – IX,CBSE Important Procedures Learn Math for Free. Visit www.ganitgurooz.com MB0904: Linear Equations in Two variables How to find a solution from the graph of a linear equation in 2 variables? :Select any point on the line in the graph.Step1 :Draw a vertical line from the point to intersect the -axis.xStep2 :Note the point where it intersects the -axis.xStep3 :Draw a horizontal line from the point to intersect the -axis.yStep4 :Note the point where it intersects the -axis.yStep5 :A solution of the equation is , .Here is obtained in step 3 and in step 5.x y x yStep6 Topic: Solution of a Linear Equation
- 25. How to draw the graph of a linear equation in 2 variables? Class – IX,CBSE Important Procedures Learn Math for Free. Visit www.ganitgurooz.com MB0904: Linear Equations in Two variables Topic: Graph of a Linear Equation
- 26. How to draw the graph of a linear equation in 2 variables? Class – IX,CBSE Important Procedures Learn Math for Free. Visit www.ganitgurooz.com :Write the equation in standard form 0 .ax by cStep1 MB0904: Linear Equations in Two variables Topic: Graph of a Linear Equation
- 27. How to draw the graph of a linear equation in 2 variables? Class – IX,CBSE Important Procedures Learn Math for Free. Visit www.ganitgurooz.com MB0904: Linear Equations in Two variables :Write the equation in standard form 0 .ax by cStep1 :Put 0 to get by 0.x cStep2 Topic: Graph of a Linear Equation
- 28. How to draw the graph of a linear equation in 2 variables? Class – IX,CBSE Important Procedures Learn Math for Free. Visit www.ganitgurooz.com MB0904: Linear Equations in Two variables How to draw the graph of a linear equation in 2 variables? :Write the equation in standard form 0 .ax by cStep1 :Put 0 to get by 0.x cStep2 :Solve this equation to get . c y b Step3 Topic: Graph of a Linear Equation
- 29. How to draw the graph of a linear equation in 2 variables? Class – IX,CBSE Important Procedures Learn Math for Free. Visit www.ganitgurooz.com MB0904: Linear Equations in Two variables :Write the equation in standard form 0 .ax by cStep1 :Put 0 to get by 0.x cStep2 :Solve this equation to get . c y b Step3 :Now put 0 in the equation in step 1 to get 0.y ax cStep4 Topic: Graph of a Linear Equation
- 30. How to draw the graph of a linear equation in 2 variables? Class – IX,CBSE Important Procedures Learn Math for Free. Visit www.ganitgurooz.com MB0904: Linear Equations in Two variables :Write the equation in standard form 0 .ax by cStep1 :Put 0 to get by 0.x cStep2 :Solve this equation to get . c y b Step3 :Now put 0 in the equation in step 1 to get 0.y ax cStep4 :Solve this equation to get . c x a Step5 Topic: Graph of a Linear Equation
- 31. How to draw the graph of a linear equation in 2 variables? Class – IX,CBSE Important Procedures Learn Math for Free. Visit www.ganitgurooz.com MB0904: Linear Equations in Two variables :Write the equation in standard form 0 .ax by cStep1 :Put 0 to get by 0.x cStep2 :Solve this equation to get . c y b Step3 :Now put 0 in the equation in step 1 to get 0.y ax cStep4 :Solve this equation to get . c x a Step5 :You have two solutions 0, and ,0 . c c b a Step6 Topic: Graph of a Linear Equation
- 32. How to draw the graph of a linear equation in 2 variables? Class – IX,CBSE Important Procedures Learn Math for Free. Visit www.ganitgurooz.com MB0904: Linear Equations in Two variables :Join these points to obtain a line.Step8 How to draw the graph of a linear equation in 2 variables? :Locate and plot the points 0, and ,0 n a coordinate plane (on a graph paper). c c b a Step7 Topic: Graph of a Linear Equation
- 33. How to draw the graph of a linear equation in 2 variables? Class – IX,CBSE Important Procedures Learn Math for Free. Visit www.ganitgurooz.com MB0904: Linear Equations in Two variables :Join these points to obtain a line.Step8 How to draw the graph of a linear equation in 2 variables? :Locate and plot the points 0, and ,0 n a coordinate plane (on a graph paper). c c b a Step7 :Join these points to obtain a line.Step8 Topic: Graph of a Linear Equation