For the two linear equation 2 x -3 y - k and 6 x -9 y -12- which among the given statement is correct-A- If k-4- coincident lines with many solutionB- If k -36- parallel lines with no solutionC- Both a and bD- None of these

The correct option is C Both (a) and (b)2x+3y=k and 6x+9y=12 a_1=2, b_1=3, c_1=k a_2=6, b_2=9, c_2=12 a_1a_2=26, b_1b_2=39, c_1c_2=k12 If k=4, a_1a_2=b_1b_2=c_ ...

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Standard X

Mathematics

Equation Reducible to Linear Equations in Two Variables

For the two l...

Question

For the two linear equation $2 x + 3 y = k$ and $6 x + 9 y = 12$ , which among the given statement is correct?

If k = 4, coincident lines with many solution

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If k = 36, parallel lines with no solution

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Both (a) and (b)

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None of these

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Solution

The correct option is C Both (a) and (b)
$2 x + 3 y = k$ and $6 x + 9 y = 12$
$a_{1} = 2, b_{1} = 3, c_{1} = k$
$a_{2} = 6, b_{2} = 9, c_{2} = 12$
$\frac{a_{1}}{a_{2}} = \frac{2}{6}, \frac{b_{1}}{b_{2}} = \frac{3}{9}, \frac{c_{1}}{c_{2}} = \frac{k}{12}$
If $k = 4, \frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$ i.e. lines are coincident and have many solutions
If $k = 36, \frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$ i. e. lines are parallel and have no solution.

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For the two linear equation 2x+3y=k and 6x+9y=12, which among the given statement is correct?

The correct option is C Both (a) and (b)2x+3y=k and 6x+9y=12 a1=2,b1=3,c1=k a2=6,b2=9,c2=12 a1a2=26,b1b2=39,c1c2=k12 If k=4,a1a2=b1b2=c1c2 i.e. lines are coincident and have many solutions If k=36,a1a2=b1b2≠c1c2 i. e. lines are parallel and have no solution.

For the two linear equation $2 x + 3 y = k$ and $6 x + 9 y = 12$ , which among the given statement is correct?