Question

check whether pair of linear equations x+y=5 and 2x+y=10 are consistent​

Answer 1

Check whether $x+y=5$ and $2x+y=10$ are consistent

Definition:

A consistent system of equations is one that has at least one solution,that is if there is at least one set of values for the unknowns that satisifes each equation in the system.

Step-by-step explanation:

$x+y=5$     (1)

$2x+y=10$   (2)

Equation (1) cannot be simplefied further ,whereas equation (2) ,if we assume to divide the equation by 2,it may lead to same as equation (1) but we cannot divide the equation (2) by 2,as the variable of y is 1,dividing by 2 leads to 1/2 ,so the equation (2) becomes,

$x+\frac{1}{2}y=5$

Which is not same as equation(1)

Therefore,the given pair of equations does not have any solution,so the system is not consistent.