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Graphical Method to find the Solution of Pair of Linear Equation in Two Variables

Graphical Method to find the Solution of Pair of Linear Equation in Two Variables. Sketching straight lines Solving Pair of linear equations in two variables by straight line graphs Graphical Method. Sketching straight lines. Table of values.

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Graphical Method to find the Solution of Pair of Linear Equation in Two Variables

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  1. Graphical Method to find the Solution of Pair of Linear Equation in Two Variables

  2. Sketching straight lines • Solving Pair of linear equations in two variables by straight line graphs Graphical Method

  3. Sketching straight lines Table of values To draw the graph of a straight line we must find the coordinates of some points which lie on the line.We do this by forming a table of values . Give the x coordinate a value and find the corresponding y coordinate for several points Make a table of values for the equation y = 2x + 1 2 3 0 1 3 1 5 7 So (0,1) (1,3) (2,5) and (3,7) all lie on the line with equation y=2x + 1 Now plot the points and join them up

  4. . y Plot the points (0,1) (1,3) (2,5) and (3,7) on the grid 7 6 5 4 3 2 1 . Now join then up to give a straight line . . x 0 1 2 3 4 All the points on the line satisfy the equation y = 2x + 1

  5. Sketching lines by finding where the lines cross the x axis and the y axis A quicker method Straight lines cross the x axis when the value of y = o Straight lines cross the y axis when the value of x =0 Sketch the line 2x + 3y = 6 Line crosses x axis when y = 0 Line crosses y axis when x = 0 2x + 0 =6 0 + 3y = 6 3y =6 2x =6 y = 2 x =3 at ( 3,0) at ( 0,2)

  6. Plot 0,2) and (3,0) and join them up with a straight line y 7 6 5 4 3 2 1 Now join then up to give a straight line . . x 0 1 2 3 4 All the points on the line satisfy the equation 2x + 3y = 6

  7. Solving Pair of linear equations in two variables by straight line graphs (Graphical Method)

  8. y 10 9 8 Plot 6 2x – y = 8 Example 1 5 4 x – y = 1 3 2 1 x 0 -10 1 2 3 4 5 6 7 9 10 -9 -8 -6 -4 -3 -2 8 -7 -5 -1 -1 -2 -3 -4 -5 -6 -7  -8 -9 -10 Graphical Solution of pair of linear equations in two variables Graphical representation of pair of linear Equations as two lines. y = 2x - 8 y = x - 1

  9. y 10 9 8 7 6 5 4 3 2 1 x 0 -10 1 2 3 4 5 6 7 9 10 -9 -8 -6 -4 -3 -2 8 -7 -5 -1 -1 -2 -3 -4 -5 -6 Example 2 -7 Solve -8 -9 -2x -y = -1  -10 -4x +2y = 2 Graphical Solution of pair of linear equations in two variables • Graphical representation of pair of linear Equations as two lines. y = 2x + 1 y = (4x + 2)/2

  10. y 10 9 8 7 6 Question 5 4 -x + y = 3 3 -x + y = 6 2 1 x 0 -10 1 2 3 4 5 6 7 9 10 -9 -8 -6 -4 -3 -2 8 -7 -5 -1 -1 -2 -3 -4 -5 -6 -7 -8 -9  -10 Graphical Solution of pair of linear equations in two variables • Graphical representation of pair of linear Equations as two lines. y = x + 3 y = x + 6

  11. We have seen that the lines may intersect or may be parallel or may coincide. Can we find the solution of the pair of equations from the lines drawn that is solution from the geometrical point of view? Let us look at the earlier example one by one.

  12. y 10 Solutions x = 7, y = 6 9 8 Solve 7 6 2x – y = 8 Example 1 5 4 x – y = 1 3 2 1 x 0 -10 1 2 3 4 5 6 7 9 10 -9 -8 -6 -4 -3 -2 8 -7 -5 -1 -1 -2 -3 -4 -5 -6 -7  -8 -9 -10 Graphical Solution of pair of linear equations in two variables y = 2x - 8 y = x - 1 (7,6) The co-ordinates of the point of intersection of lines give the solutions to the equations. (7,6) is the only common point for both the intersecting lines (7,6) is the one and only one solution for the given pair of linear equations. The pair of equations has a unique solution is called consistent pair of linear equations.

  13. y 10 9 8 Solutions Infinite many solutions Coincident lines 7 6 5 4 3 2 1 x 0 -10 1 2 3 4 5 6 7 9 10 -9 -8 -6 -4 -3 -2 8 -7 -5 -1 -1 -2 -3 -4 -5 -6 Solve Example 2 -7 -8 -2x - y = -1 -9 -4x + 2y = 2 2 -10 Graphical Solution of pair of linear equations in two variables y = 2x + 1 y = (4x + 2)/2 Here graph geometrically represent a pair of coincident lines. Every point on the line is a common solution for the equations given The pair of equations has infinite many solution s. A dependent pair of linear equation s is always consistent A pair of linear equation which are equivalent has infinite many distinct common solutions are called dependent pair of linear equations

  14. y Solutions Parallel lines No solution 10 9 8 7 6 Solve Question 5 4 -x + y = 3 3 -x + y = 6 2 1 x 0 -10 1 2 3 4 5 6 7 9 10 -9 -8 -6 -4 -3 -2 8 -7 -5 -1 -1 -2 -3 -4 -5 -6 -7 -8 -9  -10 Graphical Solution of pair of linear equations in two variables y = x + 3 y = x + 6 Here graph geometrically represent a pair of parallel lines. Lines do not intersect at all The equations have no common solution. The pair of linear equations which has no solution is called an inconsistent pair of linear equation.

  15. y 10 9 8 Solutions x = 3, y = 7 7 6 5 4 3 2 1 x 0 -10 1 2 3 4 5 6 7 9 10 -9 -8 -6 -4 -3 -2 8 -7 -5 -1 -1 -2 -3 -4 -5 -6 Example 2 -7 Solve -8 -9 -2x + y = 1  -10 x + y = 10 Home Work (3,7)

  16. y 10 9 8 Solutions x = 1, y = 4 7 6 Solve Question 5 4 -x + y = 3 3 2 2x + y = 6 1 x 0 -10 1 2 3 4 5 6 7 9 10 -9 -8 -6 -4 -3 -2 8 -7 -5 -1 -1 -2 -3 -4 -5 -6 -7 -8 -9  -10 (1,4)

  17. y 10 9 8 Solutions x = 3, y = 7 7 6 5 4 3 2 1 x 0 -10 1 2 3 4 5 6 7 9 10 -9 -8 -6 -4 -3 -2 8 -7 -5 -1 -1 -2 -3 -4 -5 -6 Example 2 -7 Solve -8 -9 -2x + y = 1  -10 x + y = 10 (3,7)

  18. Presented by NikhileshShrivastava TGT(Maths) K.V.Kanker

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