Find the value(s) of p for the equations -3x | vedclass

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(D) Given,the pair of linear equations is:$-3x + 5y - 7 = 0 \dots (i)$$2px - 3y - 1 = 0 \dots (ii)$Comparing these with the standard form $ax + by + c

Vedclass · Accepted Answer

$p 
eq \frac{9}{10}$

Vedclass · Answer

(D) Given,the pair of linear equations is:$-3x + 5y - 7 = 0 \dots (i)$$2px - 3y - 1 = 0 \dots (ii)$Comparing these with the standard form $ax + by + c = 0$,we get:$a_1 = -3, b_1 = 5, c_1 = -7$$a_2 = 2p, b_2 = -3, c_2 = -1$For the lines to intersect at a unique point,the condition for a unique solution is:$\frac{a_1}{a_2} 
eq \frac{b_1}{b_2}$Substituting the values:$\frac{-3}{2p} 
eq \frac{5}{-3}$Cross-multiplying,we get:$(-3) 	imes (-3) 
eq 5 	imes (2p)$$9 
eq 10p$$p 
eq \frac{9}{10}$Thus,the lines intersect at a unique point for all real values of $p$ except $\frac{9}{10}$.

Find the value$(s)$ of $p$ for the equations $-3x + 5y = 7$ and $2px - 3y = 1$ if the lines represented by these equations intersect at a unique point.

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