Activity & Practical To Find the distance between two given points graphically.| Class 10th level | edugrown

  • Students will learn that some pairs of linear equations in two variables have a unique solution (intersecting lines), some have infinitely many solutions (coincident lines) and some have no solutions (parallel lines).

Objective

  • To verify the conditions for consistency of a system of linear equations in two variables by graphical representation.

MATERIALS REQUIRED

Graph papers, fevicol, geometry box, cardboard.

THEORY

  • In a right-angled triangle the square of hypotenuse is equal to the sum of squares on the other two sides.
  • Concept of a right-angled triangle.
  • Area of square = (side)2
  • Construction of perpendicular lines.

PROCEDURE

      1. Consider the three pairs of linear equations
        1stpair: 2x-5y+4=0, 2x+y-8 = 0
        2nd pair: 4x + 6y = 24, 2x + 3y =6
        3rd pair: x-2y=5, 3x-6y=15

        1. Take the 1st pair of linear equations in two variables, e.g., 2x – 5y +4=0, 2x +y-8 = 0.
        2. Obtain a table of at least three such pairs (x, y) which satisfy the given equations.
          NCERT Class 10 Maths Lab Manual - Linear Equations 2
        3. Plot the points of two equations on the graph paper as shown in fig. (i).
          NCERT Class 10 Maths Lab Manual - Linear Equations 3
        4. Observe whether the lines are intersecting, parallel or coincident. Write the values in observation table.
          Also, check ;\frac { { a }_{ 1 } }{ { a }_{ 2 } } ;\frac { { b }_{ 1 } }{ { b }_{ 2 } } ;\frac { { c }_{ 1 } }{ { c }_{ 2 } }
        5. Take the second pair of linear equations in two variables
          NCERT Class 10 Maths Lab Manual - Linear Equations 4
        6. Repeat the steps 3 and 4.
          NCERT Class 10 Maths Lab Manual - Linear Equations 5
        7. Take the third pair of linear equations in two variables,i.e. x-2y=5, 3x-6y=15
          NCERT Class 10 Maths Lab Manual - Linear Equations 6
        8. Repeat steps 3 and 4
          NCERT Class 10 Maths Lab Manual - Linear Equations 7

Observation

Obtain the condition for two lines to be intersecting, parallel or coincident from the observation table by
comparing the values of \frac { { a }_{ 1 } }{ { a }_{ 2 } } ,\frac { { b }_{ 1 } }{ { b }_{ 2 } } and\frac { { c }_{ 1 } }{ { c }_{ 2 } }

Students will observe that

  1. for intersecting lines, \frac { { a }_{ 1 } }{ { a }_{ 2 } } \neq \frac { { b }_{ 1 } }{ { b }_{ 2 } }
  2. for parallel lines, \frac { { a }_{ 1 } }{ { a }_{ 2 } } =\frac { { b }_{ 1 } }{ { b }_{ 2 } } \neq \frac { { c }_{ 1 } }{ { c }_{ 2 } }
  3. for coincident lines, \frac { { a }_{ 1 } }{ { a }_{ 2 } } =\frac { { b }_{ 1 } }{ { b }_{ 2 } } =\frac { { c }_{ 1 } }{ { c }_{ 2 } }

Result

The conditions for consistency of a system of linear equations in two variables is verified.

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