Question

1) Find the value of 'K' for which the pair of
linear Equation x+2y-5=0 and 3x + 6y + k represent coincident lines
.​

Answer 1

Step-by-step explanation:

x/3x=2y/6y=-5/k

1/3=1/3=-5/k

1/3=-5/k

k=-15

Answer 2

The value of k is -15.

Step-by-step explanation:

Given : Linear equations $x+2y-5=0$ and $3x + 6y + k=0$.

To find : The value of 'K' for which the pair of  linear equations represent coincident lines ?

Solution :

When the system of equation is in form $a_1x+b_1y+c_1=0, a_2x+b_2y+c_2=0=0$ then the condition for coincident lines is  

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

Comparing with given equations,

$a_1=1,\ b_1=2,\ c_1=-5,\ a_2=3,\ b_2=6,\ c_2=k$

Substitute the values,

$\frac{1}{3}=\frac{2}{6}=\frac{-5}{k}$

$\frac{1}{3}=\frac{1}{3}=-\frac{5}{k}$

Taking equation,

$\frac{1}{3}=-\frac{5}{k}$

Cross multiply,

$k=-5\times 3$

$k=-15$

Therefore, the value of k is -15.

#Learn more

Find the value of p and q for which the system of equations represent coincident lines

2x + 3y = 7, (p+q+1)x+(p+2q+2)y=4(p+q)+1