Question

e Find the value of k for which the system
of equations
5x-3y =0 and 2x+ky=0
has a non-zero solution​

Answer 1

$\large{\underline{\bf{\purple{Given:-}}}}$

• ✦ Equations :-

• 5x - 3y = 0
• 2x + ky = 0

$\large{\underline{\bf{\purple{To\:Find:-}}}}$

• ✦ Value of k

$\huge{\underline{\bf{\red{Solution:-}}}}$

The given equations are :-

• 5x - 3y =0
• 2x + ky = 0

These equations are of the form

• $\rm\:a_1x+b_1y+c_1=0$
• $\rm\:a_2x+b_2y+c_2=0$

where,

• a1 = 5
• b1 = -3

• a2 =2
• b2 = k

$: \mapsto \rm\: \frac{a_1 }{a_2} = \frac{5}{2} \: ,\:\:\frac{b_1}{b_2} = \frac{ - 3}{k} \\ \\: \mapsto \rm\:it \: is \: given \: that \: the \: equations \: have \\ \rm \: non-zero \: solution \: \\ \\ : \mapsto \rm\:then \: \frac{a_1}{a_2} = \frac{b_1}{b_2} \\ \\ : \mapsto \rm\: \frac{5}{2} = \frac{ - 3}{k} \\ \\ : \mapsto \rm\:5k = - 6 \\ \\ : \mapsto \bf\:k = \frac{ - 6}{5}$

So k = -6/5

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