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For what value of $p$ will the graphs of $2 x + 3 y = 5$ and $4 x + p y = 7$ be parallel (no solution)?

Class 10Graphical MethodAlgebra — Systems of Equations

A12
B6
C7
D5

Step-by-Step Solution

Parallel needs

\frac{a _{1}}{a _{2}} = \frac{b _{1}}{b _{2}} \neq = \frac{c _{1}}{c _{2}} : \frac{2}{4} = \frac{3}{p}

, so

p = 6

. Check

\frac{c _{1}}{c _{2}} = \frac{5}{7} \neq = \frac{1}{2}

, confirming parallel.

Answer: B) 6

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