untitled

(c) Given system of equations are : 3 x 5 y 7
6 x 10 y 15

Ratio of the coefficients of x is

6

3

or

2

1

Ratio of the coefficients of y is

10

5





or

2

1

ratio of the constant terms is
15

7

? we get,
15

7

10

5

6

3

z





Therefore, the system of equations are inconsistent and mutually independent. The
system of equations have no solution.
Activity : Verify whether the system of equations x 2 y 1 0 , 2 xy 3 0
are consistent and dependent and indicate how many solutions the system of
equations may have.

Exercise 12⋅ 1

Mention with arguments, whether the following simple simultaneous equations are
consistent/ inconsistent, mutually dependen t/ independent and indicate the number of
solutions :

1. xy 4 2. 2 xy 3 3. xy 4 0
   xy 10 4 x 2 y 6 3 x 3 y 10 0


2. 3 x 2 y 0 5. 3 x 2 y 0 6. 5 x 2 y 16 0

6 x 4 y 0 9 x 6 y 0 2

5

6

3 x y

7. 1
   2

1

 xy  8. 0

2

1

 xy 9. 1

2

1

 xy 

x 2 y 2 x 2 y 0 xy 5

10. axcy 0
    cxay c^2 a^2.
    12 ⋅3 Solution of simple sumultaneous equations
    We shall discuss the solutions of only the consistent and independent simple
    simultaneous equations. Such system of equation has only one (unique) solution.
    Here, four methods of solutions are discussed :
    (1) Method of substitution, (2) Method of elimination (3) Method of cross-
    multiplication (4) Graphical method.