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

$x\ −\ 3y\ =\ 3$
$3x\ −\ 9y\ =\ 2$

 Given: The given system of equation is $x\ −\ 3y\ =\ 3$ ; $3x\ −\ 9y\ =\ 2$

To do: Solve the system of equation and determine if the solution has unique , infinite or no solution.

Solution:

The given system of equations can be written as:

$x\ −\ 3y\ =\ 3$

$3x\ −\ 9y\ =\ 2$

The given system of equation is of form:

 $a_{1} x+b_{1} y=c_{1}\ and\ a_{2} x+b_{2} y=c_{2}$

Here,  $a_1 = 1, b_1=-3, c_1=3 \ and \ a_2=3, b_2=-9, c_2=2 $

We have,

$\frac{a_1}{a_2}=\frac{1}{3}$

$\frac{b_1}{b_2}=\frac{-3}{-9}=\frac{1}{3}$ 

$\frac{c_1}{c_2}=\frac{3}{2} $

Clearly, $\frac{a_1}{a_2}=\frac{b_1}{b_2}$ not equal to $\frac{c_1}{c_2}$ 

So, given system of equation has no solution

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Updated on: 10-Oct-2022

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