Question

For what value of ‘ p’ the following pair of linear equations have a unique solution. 2x+py=-5 and 3x+3y=-6

Answer 1

For an unique solution for a simultaneous linear equation,

$\rm \dfrac{a_1}{a_2} \neq \dfrac{b_1}{b_2} \neq \dfrac{c_1}{c_2}$

From

$\rm{}a_1x + b_1y + c_1 = 0 \\ \rm{a_2x + b_2y +c_2 = 0 }$

Here,

$2x + py = - 5 \\ 3x + 3y = - 6$

Extracting the coefficients,

$= > \frac{2}{3} \neq \frac{p}{3} \neq \frac{ - 5}{ - 6} \\ \\ \rm = > \frac{2}{3} \neq \frac{p : \{ any \: \: real \: \:number \: \: except \: \: 2 \} }{3} \neq \frac{5}{6}$

Thus,

• Value of p is {0, 1, 3, 4, ...... $\infin$}