Login/Sign Up
Home » In all the following systems of equations determine whether the system has a unique solution, no solution or infinite solutions. If In case there is a unique solution ,
In all the following systems of equations determine whether the system has a unique solution, no solution or infinite solutions. If In case there is a unique solution3x-5y=20 ,6x-10y=40
CBSE | Class 10 | Exercise 3.5 | Maths | Pair of Linear Equations In Two Variables | RD Sharma
In all the following systems of equations determine whether the system has a unique solution, no solution or infinite solutions. If In case there is a unique solution3x-5y=20 ,6x-10y=40

Given system of equations is:

3x-5y-20=0

6x-10y-40=0

Above equations are of the form

{{a}_{1}}x+{{b}_{1}}y-{{c}_{1}}=0

{{a}_{2}}x+{{b}_{2}}y-{{c}_{2}}=0

Here, {{a}_{1}}=3,{{b}_{1}}=-5,{{c}_{1}}=-20

{{a}_{2}}=6,{{b}_{2}}=-10,{{c}_{2}}=-40

According to the question, we get

{{a}_{1}}/{{a}_{2}}=3/6=1/2

{{b}_{1}}/{{b}_{2}}=-5/-10

{{c}_{1}}/{{c}_{2}}=-20/-40=1/2

\Rightarrow {{a}_{1}}/{{a}_{2}}={{b}_{1}}/{{b}_{2}}={{c}_{1}}/{{c}_{2}}

Therefore, we can close that the given equation has infinity many solutions.

i

More Material