Question

Find the value of k for which the system of equations 5x - 3y = 0, 2x + ky = 0
have infinite solutions.​

Answer 1

Answer:

k = -6/5.

Step-by-step explanation:

The given system of equations:

5x - 3y = 0.....(i)

2x + ky = 0.....(ii)

These equations are of the following form:

a1x+b1y+c1 = 0, a2x+b2y+c2 = 0

where, a1 = 5, b1= -3, c1 = 0 and a2 = 2, b2 = k, c2 = 0

For a non-zero solution, we must have:

$\frac{a1}{a2} = \frac{b1}{b2}$

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

$5k = - 6$

$k = \frac{ - 6}{5}$

Hence, the value for k = -6/5.

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Answer 2

Answer:

The given system of equations:

5x - 3y = 0 …......(i)

2x + ky = 0 …......(ii)

These equations are of the following form: a1x+b1y+ c1 = 0,

a2x+b2y+ c2 = 0

where, a1 = 5, b1= - 3, c1 = 0

and a2 = 2, b2 = k, c2 = 0

For a non-zero solution,

a1/ a2 = b1 / b2

5/ 2 = - 3 / k

by cross multiply,

5k = - 6

k = -6 /5

hence the required value of k is -6 / 5..