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# In the Following Systems of Equations Determine Whether the System Has a Unique Solution, No Solution Or Infinitely Many Solutions. in Case There is a Unique Solution, Find It: 2x + Y - 5 = 0 4x + 2y - 10 = 0 - CBSE Class 10 - Mathematics

ConceptPair of Linear Equations in Two Variables

#### Question

In the following systems of equations determine whether the system has a unique solution, no solution or infinitely many solutions. In case there is a unique solution, find it:

2x + y - 5 = 0

4x + 2y - 10 = 0

#### Solution

The given system of equation may be written as

2x + y - 5 = 0

4x + 2y - 10 = 0

The given system of equations is of the form

a_1x + b_1y + c_1 = 0

a_2x + b_2y + c_2 = 0

Where a_1 = 2, b_1 = 1, c_1 = -5

And a_2 = 4, b_2 = 2, c_2 = -10

We have

a_1/a_2 = 2/4 = 1/2

b_1/b_2 = 1/2

And c_1/c_2 = (-5)/(-10) = 1/2

cleary a_1/a_2 = b_1/b_2 = c_1/c_2

So, the given system of equation has infinity many solutions.

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Solution In the Following Systems of Equations Determine Whether the System Has a Unique Solution, No Solution Or Infinitely Many Solutions. in Case There is a Unique Solution, Find It: 2x + Y - 5 = 0 4x + 2y - 10 = 0 Concept: Pair of Linear Equations in Two Variables.
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