Question

2. Find the value of p for which the given simultaneous equations
have unique solution.

3x+y=10. 9x+py=23.

Answer 1

Given Equations :

• 3x + y = 10
• 9x + py = 23

Given :

• In the question it is given that they have a unique solution.

We know that, if 2 equations have unique solutions, it means that

$\frac{a1}{a2} ≠ \frac{b1}{b2}$

Which is,

$\frac{a1}{a2}=\frac{3}{9}$ ⟶ $\frac{1}{3}$

$\frac{b1}{b2}=\frac{1}{p}$

As we know, $\frac{a1}{a2}≠\frac{b1}{b2}$

$\frac{1}{3}≠\frac{1}{p}$

⟹ $\boxed{\sf{p ≠ 3}}$

So, we can say that except 3, any number can be the value of p.

Answer 2

Given ,

A pair of linear equations are

3x + y = 0

9x + py = 23

We know that , a pair of linear equations will have unique solution if

$\star \: \: \sf \frac{ a_{1} }{a_{2} } ≠ \frac{b_{1} }{b_{2} }$

Thus ,

$\sf \Rightarrow \frac{3}{9} ≠ \frac{1}{p} \\ \\ \sf \Rightarrow p≠3$

$\therefore \sf \bold{ \underline{For \: all \: values \: of \: p \: , \: except \: 3 \: the \: given \: eq \: will \: have \: unique \: solution }}$