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### Linear Equation In Two Variable

• 2. Letโs start with the journey with some basics here: (+,+)(-,+) (-,-) (+,-) Learning the Cartesian sign is important . This is the origin The Quadrants
• 3. The word LINEAR originates from: Today we will study the equation for lines. In a Graph, these equations are used To get the position of a line
• 4. Linear equation in two variable THE STANDARD FORM: ax+by+c=0 Here, a and b are the constants that cannot be 0 Example: 47x+7y=9c can be zero
• 5. There are 2 methods to solve A Pair of Linear equation 1 ๏  Graphical method 2 ๏  Algebraic method ax+by+c=0
• 6. Lets solve some examples quickly: Q. We need to plot the diagram for 5x+4y+20=0 and check whether (0,-5) lies in it. STEP 1: Assume a value for x and find the value of y x y We will take three observation to plot the point. Lets take the points -1,0,1 for x When x=-1 5(-1)+4y+20=0 .โ.-5+4y=-20 .โ.4y=-20+5 y=-15/4=-3.75 When x=0 5(0)+4y+20=0 .โ.4y=-20 .โ.y=-20/4 y=-5 When x=-1 5(1)+4y+20=0 .โ.5+4y=-20 .โ.4y=-20-5 y=-25/4=-6.25 -1 -3.75 0 -5 1 -6.25
• 7. x -1 0 1 y -3.75 -5 -6.25 From this observation We come to know that (0,-5) Lies on the line Now lets plot our graph This is our graph based on Cartesian sign Remember to label The points and the line (0,-5) (-1,-3.75) (1,-6.25) (0,0) And we are done!
• 8. The standard form: ax+bx+c=0 x+y=5 ๏ x+y-5=0 3x+7y-66=0 8y-4x=-12 ๏  -4x+8y+12=0 2x+ ๐ ๐ ๐ฒ = ๐ ๏  2x+ ๐ ๐ ๐ฒ โ ๐ =0 Lets do some quick activity: Determine the coefficints and the constants from the given expressions a b c 1 1 -5 3 7 -66 8 -4 12 2 ๐ ๐ -7
• 9. Quick facts: For the equations like: x=n, where n can be any integer. The line on the graph will always be Parallel to y-axis Examples: X=-5 X=3 X=6 X=-2 Theyโre parallel to y-axis Y-axis X-axis
• 10. Quick facts: For the equations like: y=n, where n can be any integer. The line on the graph will always be Parallel to x-axis Examples: y=-5 y=3 y=6 y=-2 Theyโre parallel to x-axis Y-axis X-axis
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