Question

Find the value of k for which the system of linear equation 2x+5y=3 ,3[k+1]x+2[k+2]y=2k will haveinfinite number of solution

Answer 1

this is the answer but not sure

Answer 2

Answer:

Value of k is 3.

Step-by-step explanation:

Given System of equation,

2x + 5y = 3

( k + 1 )x + 2( k + 2 )y = 2k

System of equation has Infinite number of solutions.

To find: Value of k

We know that when solution of system of equation is infinite then ratio is as follows,

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

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

Consider,

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

2 × 2k = 3 ( k + 1 )

4k = 3k + 3

4k - 3k = 3

k = 3

Therefore, Value of k is 3.