Question

If the lines represented by the pair of linear equations 2x+5y = 3 and
(k+1)x +2(k+2)y = 2k are coincident, then find the value of k.

Answer 1

Here is your answer

Answer 2

Answer:

The value of k=3

Step-by-step explanation:

Given : If the lines represented by the pair of linear equations $2x+5y=3$ and   $(k+1)x +2(k+2)y = 2k$ are coincident.

To find : The value of k?

Solution :

When two lines are coincident then the ratio of their coefficient are equal

i.e, $\frac{a_1}{a_2} =\frac{b_1}{b_2} =\frac{c_1}{c_2}$

In the given lines,

$a_1=2 , a_2=k+1\\b_1=5 ,b_2=2(k+2)\\c_1=3,c_2=2k$

Substitute the value in the formula,

$\frac{2}{k+1} =\frac{5}{2(k+2)} =\frac{3}{2k}$

Now, we take any two coefficient and solve them

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

Cross multiply

$2\times 2k=3\times (k+1)}$

$4k=3k+3$

$k=3$

Therefore, The value of k is 3.