Question

Activity To obtain the conditions for consistency of a system of linear equations in two variables given below

x-2y=0 and 3x+4y-20=0
2x+3y-9=0 and 4x+6y-18=0
x+2y-4=0 and 2x+4y-12=0​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

OBJECTIVE

To use the graphical method to obtain the conditions of consistency and hence to solve a given system of linear equations in two variables

Materials Required

1.)Three sheets of graph paper

2.)A ruler

3.)A pencil

Step-by-step explanation:

Theory

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

2.)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.

3.)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.

x 1 3

y 1 0

Similarly, from equation (ii), we have

y=1/3( 2 – 4x).

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 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

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