Check if $x - 3 y - 7 = 0$ and $3 x - 3 y - 15 = 0$ has unique/infinite/no solution.

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Solution

$x - 3 y - 7 = 0, 3 x - 3 y - 15 = 0$
i.e $x - 3 y - 7 = 0$ $3 (x - y - 5) = 0$
Here both equations are different in respect of coefficient of $y$ and constant term, so it has unique solution. We need not to check
$\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}, \frac{c_{1}}{c_{2}}$

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x - 3 y - 7 = 0, 3 x - 3 y - 15 = 0

Which of the following pairs of linear equations has unique solution, no solution or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method.

Determine whether the system of linear equations

2 x + 3 y - 5 = 0, 6 x + 9 y - 15 = 0

has a unique solution, no solutions, or an infinite number of solutions.

The system of pair of equations $4 x - 3 y + 12 = 0$ and $2 x + 3 y - 15 = 0$ has

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Check if x−3y−7=0 and 3x−3y−15=0 has unique/infinite/no solution.

x−3y−7=0,3x−3y−15=0i.e x−3y−7=0 3(x−y−5)=0Here both equations are different in respect of coefficient of y and constant term, so it has unique solution. We need not to checka1a2,b1b2,c1c2

Check if $x - 3 y - 7 = 0$ and $3 x - 3 y - 15 = 0$ has unique/infinite/no solution.

$x - 3 y - 7 = 0, 3 x - 3 y - 15 = 0$
i.e $x - 3 y - 7 = 0$ $3 (x - y - 5) = 0$
Here both equations are different in respect of coefficient of $y$ and constant term, so it has unique solution. We need not to check
$\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}, \frac{c_{1}}{c_{2}}$