Question

The value of k for which the pair of linear equations 3x+4y+5=0 and 12x+2ky+17=0 has no solution​

Answer 1

Solution :

We have two linear pair equations :

• 3x + 4y + 5 = 0
• 12x + 2ky + 17 = 0

As we know that given equations compared with by ;

$\bullet\sf{a_1x + b_1y + c_1 = 0}$

$\bullet\sf{a_2x + b_2y + c_2 = 0}$

$\underline{\underline{\tt{According\:to\:the\:question\::}}}$

• 3x + 4y = -5
• 12x + 2ky = -17

As we know that formula of the no solution;

$\boxed{\bf{\frac{a_1}{a_2} =\frac{b_1}{b_2} \neq \frac{c_1}{c_2} }}$

• a1 = 3
• b1 = 4
• b2 = 2k
• c1 = -5
• c2 = -17

Now;

$\longrightarrow\tt{\dfrac{a_1}{a_2} =\dfrac{b_1}{b_2} \neq \dfrac{c_1}{c_2} }$

$\longrightarrow\tt{\dfrac{3}{12} =\dfrac{4}{2k} \neq \dfrac{-5}{-17} }$

$\longrightarrow\tt{\dfrac{3}{12} =\dfrac{4}{2k} \:\:\& \:\: \dfrac{4}{2k} \neq \dfrac{-5}{-17} }$

$\longrightarrow\tt{\dfrac{3}{12} =\dfrac{4}{2k}}$

$\longrightarrow\tt{6k = 48\:\:\underbrace{\sf{cross-multiplication}}}$

$\longrightarrow\tt{k=\cancel{48/6}}$

$\longrightarrow\bf{k=8}$

Thus;

The value of k will be 8 .