Question

2x+3y -5=0,6x+k=0 have infinate many solutions then find value of k

Answer 1

Answer:

k = 9

Step-by-step explanation:

When the following have infinitely many solutions,

$\frac{a1}{a2} = \frac{b1}{b2} = \frac{c1}{c2}$

$\frac{2}{6} = \frac{3}{k}$

2k = 18

$k = \frac{18}{2}$

k = 9

Answer 2

ANSWER:-

$2x + 3y - 5 = 0 \: and \: 6x + k = 0$

$= > 2x + 3y - 5 = 0 \: and \: 6x + 0y + k = 0$

$= > compare \: it \: with \: ax + by + c = 0$

so,

$a_{1} = 2 \: \: b_1= 3 \: \: c_1 = - 5 \\ a_2 = 6 \: b_2 = 0 \: c_2 = k$

now,

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

$\frac{3}{0} = \frac{ - 5}{k}$

cross multiply this,

$3k = 0$

$k = \frac{0}{3} = 0$

so, the value of $\boxed{k=0}$