Question

Comment about following pair of equation:-
2x + 3y = 5
6x + 9y = 6​

Answer 1

Answer:

$\bold {According \: to \: Question}$

2x + 3y = 5.....(1)

6x +9y = 6......(2)

2x + 3y -5 = 0......(3)

6x + 9y -6 = 0......(4)

Comparing with $\frac {a1}{a2}$ ; $\frac {b1}{b2}$ ; $\frac {c1}{c2}$ , we get:-

$\frac {2}{6}$ ; $\frac {3}{9}$ ; $\frac {-5}{-6}$

$\frac {1}{3}$ = $\frac {1}{3}$ =\= $\frac {5}{6}$

Therefore, The answer is Parallel lines with no solution.

$\tt {Additional \: Information}$

• If a pair of equations are $\frac {a1}{a2}$ is not equal to $\frac {b1}{b2}$then the pair of equations are interesting lines with unique solution.

• If a pair of equations are $\frac {a1}{a2}$ is equal to $\frac {b1}{b2}$ is equal to $\frac {c1}{c2}$ , then the pair of equations are coincident lines with infinitity many solution.

• If a pair of equations are $\frac {a1}{a2}$ is equal to $\frac {b1}{b2}$ is not equal to $\frac {c1}{c2}$ , then the pair of equations are parallel lines with no solution.

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Answer 2

$\huge\star{\underline{\mathtt{\red{A}\pink{N}\green{S}\blue{W}\purple{E}\orange{R}}}}$

2x + 3y = 5.....(1)

6x +9y = 6......(2)

2x + 3y -5 = 0......(3)

6x + 9y -6 = 0......(4)

Comparing with \frac {a1}{a2} ; \frac {b1}{b2} ; \frac {c1}{c2} , we get:-

\frac {2}{6} ; \frac {3}{9} ; \frac {-5}{-6}

\frac {1}{3} = \frac {1}{3} =\= \frac {5}{6}

Therefore, The answer is Parallel lines with no solution.

\tt {Additional \: Information}

• If a pair of equations are \frac {a1}{a2} is not equal to \frac {b1}{b2}then the pair of equations are interesting lines with unique solution.

• If a pair of equations are \frac {a1}{a2} is equal to \frac {b1}{b2} is equal to \frac {c1}{c2} , then the pair of equations are coincident lines with infinitity many solution.

• If a pair of equations are \frac {a1}{a2} is equal to \frac {b1}{b2} is not equal to \frac {c1}{c2} , then the pair of equations are parallel lines with no solution.

Hope it helps✌️