# 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: X − 3y = 3 3x − 9y = 2 - Mathematics

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:

x − 3y = 3
3x − 9y = 2

#### Solution

The given system of equations may be written as

x - 3y -3 = 0

3x - 9y - 2 = 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 = 1, b_1 = -3, c_1 = -3

And a_2 = 3, b_2 = -9, c_2 = -2

We have

a_1/a_2 = 1/3

b_1/b_2 = (-3)/(-2) = 3/2

And c_1/c_2 = (-3)/(-2) = 3/2

Clearly, a_1/a_2 = b_1/b_2 != c_1/c_2

So, the given system of equation has no solutions.

Concept: Pair of Linear Equations in Two Variables
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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 3 Pair of Linear Equations in Two Variables
Exercise 3.5 | Q 1 | Page 73