If the lines given by $3 x + 2 y = 2 a n d 2 x + 5 y + 1 = 0$ are parallel then the value of k is

(a) $\frac{- 5}{4}$ (b) $\frac{2}{5}$ (c) $\frac{3}{2}$ (d) $\frac{15}{4}$

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Solution

Condition for two lines $a_{1} x + b_{1} y + c_{1} = 0 a n d a_{2} x + b_{2} y + c_{2} = 0$ to be parallel is

$\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$

Given lines are $3 x + 2 y = 2 a n d 2 x + 5 y + 1 = 0$

$a_{1} = 3, b_{1} = 2 k, c_{1} = - 2, a_{2} = 2, b_{2} = 5, c_{2} = - 1$

Using these values,

$\frac{3}{2} = \frac{2 k}{5} 4 k = 15 k = \frac{15}{4}$

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If the lines given by 3x + 2ky = 2 and 3x + 5y = 1 are parallel, then the value of k is
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If the lines given by 3x+2y=2 and 2x+5y+1=0 are parallel then the value of k is (a) −54 (b) 25 (c) 32 (d) 154

Condition for two lines a1x+b1y+c1=0 and a2x+b2y+c2=0 to be parallel is a1a2=b1b2≠c1c2 Given lines are 3x+2y=2 and 2x+5y+1=0 a1=3,b1=2k,c1=−2,a2=2,b2=5,c2=−1 Using these values, 32=2k54k=15k=154

If the lines given by $3 x + 2 y = 2 a n d 2 x + 5 y + 1 = 0$ are parallel then the value of k is

(a) $\frac{- 5}{4}$ (b) $\frac{2}{5}$ (c) $\frac{3}{2}$ (d) $\frac{15}{4}$