Find the value of p if the lines represented | vedclass

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(B) The given pair of linear equations is:$3x - y - 5 = 0$ ... $(i)$$6x - 2y - p = 0$ ... $(ii)$Comparing these with the general form $ax + by + c = 0

Vedclass · Accepted Answer

$p 
eq 10$

Vedclass · Answer

(B) The given pair of linear equations is:$3x - y - 5 = 0$ ... $(i)$$6x - 2y - p = 0$ ... $(ii)$Comparing these with the general form $ax + by + c = 0$,we get:$a_1 = 3, b_1 = -1, c_1 = -5$$a_2 = 6, b_2 = -2, c_2 = -p$For two lines to be parallel,the condition is $\frac{a_1}{a_2} = \frac{b_1}{b_2} 
eq \frac{c_1}{c_2}$.Substituting the values,we get:$\frac{3}{6} = \frac{-1}{-2} 
eq \frac{-5}{-p}$$\frac{1}{2} = \frac{1}{2} 
eq \frac{5}{p}$For the lines to be parallel,we must have $\frac{1}{2} 
eq \frac{5}{p}$.Cross-multiplying,we get $p 
eq 10$.Thus,the lines are parallel for all real values of $p$ except $10$.

Find the value of $p$ if the lines represented by the equations $3x - y - 5 = 0$ and $6x - 2y - p = 0$ are parallel.

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