Question

To obtain the conditions for consistency of a system of linear equations in two variables by graphical method
Materials required: - 3 graph papers, ruler, pencil.
Pre-requisite knowledge
Plotting of points on a graph paper
Procedure
1. Consider the three pairs of linear equations
1st pair: 2x - 3y = 3, 3x - 4y = 5
2nd Pair: 3x - y = 2, 9x - 3y = 6
3rd Pair: x +2 y - 4 = 0, x + 2y - 6 = 0
2. Take each pair of linear equations in two variables and obtain a table of at leasr three such pairs (x,y) which satisfy the given equations.
3. Plot the points corresponding to each pair of linear equations in the same graph
4. Observe whether the graph of each pair of equations is intersecting, coincident or parallel and also check 12, 12, 12
5. Obtain the condition for two lines to be intersecting, paralle or coincident from the observation table by compaing the values of 12, 12, 12

Answer 1

Step-by-step explanation:

so here's ur simple answer

Answer 2

Materials Required

Three sheets of graph paper

A ruler

A pencil

Theory

The lines corresponding to each of the equations given in a system of linear equations are drawn on a graph paper. Now,

if the two lines intersect at a point then the system is consistent and has a unique solution.

if the two lines are coincident then the system is consistent and has infinitely many solutions.

if the two lines are parallel to each other then the system is inconsistent and has no solution.

Procedure

We shall consider a pair of linear equations in two variables of the type

a1x +b1y = c1

a2x +b2y = c2

Step 1: Let the first system of linear equations be

x + 2y = 3 … (i)

4x + 3y = 2 … (ii)

Step 2: From equation (i), we have

y= ½(3 – x).

Find the values of y for two different values of x as shown below.

Step 4: Record your observations in the first observation table.

Step 5: Consider a second system of linear equations:

x – 2y = 3 … (iii)

-2x + 4y = -6 … (iv)

Step 6: From equation (iii), we get

x 3 1

y 0 -l

From equation (iv), we get

x -3 -1

y -3 -2

Draw lines on graph paper II using these points and record your observations in the second observation table.

x 1 3

y 1 0

Similarly, from equation (ii), we have

y=1/3( 2 – 4x).

Then

x -1 2

y 2 -2

Step 3: Draw a line representing the equation x+2y = 3 on graph paper I by plotting the points (1,1) and (3,0), and joining them.

Similarly, draw a line representing the equation 4x + 3y = 2 by plotting the points (-1, 2) and (2, -2), and joining them

Step 7: Consider a third system of linear equations:

2x – 3y = 5 …(v)

-4x + 6y = 3 … (vi)

Step 8: From equation (v), we get

x 1 4

y -1 1

From equation (vi), we get

x 0 3

y ½ 5/2

Draw lines on graph paper III using these points and record your observations in the third observation table.

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