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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 solution 2x + y = 5, 4x + 2y = 10
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 solution 2x + y = 5, 4x + 2y = 10

Given system of equations are:

2x + y - 5 = 0

4x + 2y - 10 = 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

Therefore, {{a}_{1}}=2,{{b}_{1}}=1,{{c}_{1}}=-5

{{a}_{2}}=4,{{b}_{2}}=2,{{c}_{2}}=-10

According to the question, we get

{{a}_{1}}/{{a}_{2}}=2/4=1/2

{{b}_{1}}/{{b}_{2}}=1/2

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

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

Accordingly, we can conclude that given equation has infinity many solutions.

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