Question

The value of k for which the equations 3x - y + 8 = 0 and 6x - ky = - 16 represent coincident lines is *
1 point

Answer 1

Answer :

The value of k is 2

Given :

The pair of equation given :

• 3x - y + 8 = 0
• 6x - ky = -16
• The given pair of equation represents coincident lines.

To Find :

• The value of k

Formulae to be used :

If the pair of equations represent coincident lines that means there is infinitely many solutions and the coefficients of the equation are related as :

$\sf \bullet \: \: \dfrac{a_{1}}{a_{2}} = \dfrac{b_{1}}{b_{2}} = \dfrac{c_{1}}{c_{2}}$

Solution :

Considering the pair of equations as :

$\sf 3x - y + 8 = 0 ..........(1) \\\\ \sf and \\ \sf 6x - ky = -16 \\\\ \sf \implies 6x - ky + 16 = 0..........(2)$

Since the pair of equation represents coincident lines so there is infinitely many solutions :

$\sf \dfrac{3}{6} = \dfrac{-1}{-k} = \dfrac{8}{16}$

Taking one pair from above we have :

$\sf \implies \dfrac{3}{6}= \dfrac{-1}{-k} \\\\ \sf \implies \dfrac{1}{2} = \dfrac{1}{k} \\\\ \sf \implies k = 2$

Answer 2

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$\huge\tt{GIVEN:}$

• Equation, 3x - y + 8 = 0 and 6x - ky = - 16
• The equation represents coincident lines.

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$\huge\tt{TO~FIND:}$

• The value of k

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$\huge\tt{FORMULAS~USED:}$

• The concident lines i.e., a pair of equations showing that there is infinite soultion possibilities and coefficients are related as - a¹/a² = b¹/b² = c¹/c²................

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$\huge\tt{SOLUTION:}$

We have both equations,

↪3x - y + 8 = 0 ____(EQ.1)

↪6x - ky = - 16 _____(EQ.2)

↪3/6 = -1/-k = 8/16

Taking equation from the pairs,

↪3/6 = -1/-k

↪1/2 = 1/k (both negative signs being cancelled by each other)

↪2 = k

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