Question

Find how many solutions does pair of linear equations 2x-3y=1 and 3x-2y-4 have

Answer 1

a1/a2=2/3
b1/b2=3/2
a1/a2is not equal to b1/b2
so the both lines will intersect at only one point

Answer 2

Concept

Linear equations in two variables can be solved to determine the values of variables .

Given

The linear equations in two variables given are  :

$2x-3y=1\\3x-2y=4$

Find

How many solutions does it contains.

Solution

We know ,

For the  pair of equations  $a_{1} x+b_{1}y + c_{1}=0$ and $a_{2} x+b_{2}y +c_{2} =0$ ,

the relation between $\frac{a_{1}}{a_{2}}$  and $\frac{b_{1}}{b_{2}}$ determines the number of possible of solutions.

if  $\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$ , then there exist one and unique solution for the pair of equations.

Since ,  $\frac{2}{3 } \neq \frac{3}{2 }$ , it means the pair of linear equations has exactly one solution.

Hence, the pair of linear equations 2x-3y=1 and 3x-2y=4 has only one unique solution.

#SPJ3