In the following system of equation determine whether the system … - Vidyadip

Question

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

$x - 3y = 3$

$3x - 9y = 2$

✓

Answer

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_1 x+b_1 y+c_1=0$
$ a_2 x+b_2 y+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,
$\frac{\text{a}_1}{\text{a}_2}=\frac{1}{3}$
$\frac{\text{b}_1}{\text{b}_2}=\frac{-3}{-9}=\frac{1}{3}$
And $\frac{\text{c}_1}{\text{c}_2}=\frac{-3}{-2}=\frac{3}{2}$
Clearly, $\frac{\text{a}_1}{\text{a}_2}=\frac{\text{b}_1}{\text{b}_2}\neq\frac{\text{c}_1}{\text{c}_2}$
So, the given system of equation has no solutions.

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