Question

Check the linear equation given below are consistent/inconsistent.
$x+y=5$ and $2x+2y=10$

Answer 1

Given linear equations are:

$x+y=5\dots .\left(1\right)$ and

$2x+2y=10\dots .\left(2\right)$

or equation (2) can be written as:

$2(x+y)=10$ or $x+y=5\dots .\left(3\right)$

solving equation (1) and (3)

As these two lines are identical.

we have infinite solutions which satisfy this system of equations.

So, the given linear equations are consistent .