Question

Which of the following pairs of linear equations has unique solution, no solution or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method

2x + y = 5

3x + 2y = 8

Answer 1

2x + y = 5

3x + 2y = 8

`a_1/a_2=2/3, b_1/b_2=1/2, c_1/c_2=(-5)/-8`

`a_1/a_2 = b_1/b_2`

Therefore, they will intersect each other at a unique point and thus, there will be a unique solution for these equations.

By cross-multiplication method,

`x/(b_1c_2-b_2c_1) = y/(c_1a_2-c_2a_1)= 1/(a_1b_2-a_2b_1)`

`x/(-8-(-10))=y/(-15+16)=1/(4-3)`

`x/2=y/1=1`

x/2=1, y/1=1

x=2, y = 1

∴ x =2, y =1