Question

if the pair of equations 2x + 3y = 7 and kx + y = 12 has no solution, then the value of k is?​

Answer 1

Answer:

2/3

Step-by-step explanation:

If the equations have no solution then it means that the lines are parallel

For parallel lines -

a1/a2 = b1/b2 ≠ c1/c2

So,

2/k = 3/1

=> k = 2/3

Answer 2

Given,

The pair of equations $2x+3y=7$ _____(1)

$kx+y=12$ _____(2)

Here, $a_{1}=2,b_{1} =3,c_{1}=7$

$a_{2} =k,b_{2}=1 ,c_{2}=12$

The pair of equations has no solutions, so these equations called as parallel line equations.

For no common solution,

$\frac{a_{1} }{a_{2}}=\frac{b_{1} }{b_{2} }\neq \frac{c_{1} }{c_{2} }$

$\frac{2}{k}=\frac{3}{1}\neq \frac{7}{12}$

$\frac{2}{k}=\frac{3}{1}$

$k=\frac{2}{3}$

Therefore, the value of $k$ is $\frac{2}{3}$.