find out whether the pair of linear equation,x=y and x-2=y-2 are consistent or inconsistent
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Given:
The two equations are x= y and x- 2= y- 2
To Find:
We have to check the given pair of equations are consistent or inconsistent.
Solution:
A consistent system of the equation is the one that has at least one solution while an inconsistent system of the equation has no solution.
Consider the first equation, x = y ·················· Eq.1 which has an infinite number of solutions.
Then, consider the second equation and simplify it.
x - 2 = y - 2
⇒ x = y ·················· Eq.2 which has an infinite number of solutions.
Since both the equations are the same, the lines will intersect at every point.
∴ The pair of equations given are consistent
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