Question

Show that a pair of linear equations 7x+y=10 & x+7y=10 are consistent

Answer 1

Hi !

7x + y = 10

x + 7y = 10

For a pair of linear equations to be consistent , it must have :-
1)Either one unique solution
OR
2)Infinitely many solutions 

We can check whether the given pair of equations have infinitely many solutions or unique solutions , by examining their coefficients !

7x + y = 10
7x + y - 10 = 0
a₁ = 7 , b₁ = 1 , c₁= -10

x + 7y = 10
x + 7y - 10 = 0
a₂ = 1 , b₂ = 7 , c₂ = -10

For a pair of  linear equations to have unique solutions :-
a₁/a₂ ≠ b₁/b₂

Lets check whether the condition is true , if its is true , then the equations would have unique solutions , and therefore it would be consistent.

7/1 ≠ 1/7

This condition is true !
Hence , the given pair of linear equations has unique solution !
Hence , they are consistent !

Answer 2

Hey there!

The two linear equations are

7x+y=10 => 7x+y-10=0

x +7y =10 => x+7y-10=0

Here

a1=7, b1 = 1,c1=-10

a2=1, b2=7, c2=-10

So

Here

7/1≠1/7

a1/a2≠ b1/b2

The system is consistent & have unique solution.

Hope helped!