In the following system of equation determine whether the system has a unique solution, no solution or infinitely many solutions. $3x+4y=52;\ 9x-6y=215$. 

Given: The system of linear equations: $3x+4y=52;\ 9x-6y=215$.

To do: To determine whether the system has a unique solution, no solution or infinitely many solutions.

Solution:

Given system of equations $3x+4y=52;\ 9x-6y=215$.

Here $a_1=3,\ b_1=4,\ c_1=52$ and $a_2=9,\ b_2=-6,\ c_2=215$

$\frac{a_1}{a_2}=\frac{3}{9}=\frac{1}{3}$

$\frac{b_1}{b_2}=\frac{4}{-6}=-\frac{2}{3}$

Here, $\frac{a_1}{a_2}≠\frac{b_1}{b_2}$

Therefore, the given system of equations has one unique solution.

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Updated on: 10-Oct-2022

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