Show that the system of equations - x + 2y + 2 = 0 and has a unique solution.
Given: - x + 2y + 2 = 0 and
To Prove: The system of given equations has a unique solution.
Proof:
We know that the general form for a pair of linear equations in 2 variables x and y is a1x + b1y + c1 = 0
and a2x + b2y + c2 = 0.
Comparing with above equations,
we have a1 = - 1,
b1 = 2,
c1 = 2;
a2 = 1/2 ,
b2 = - 1/2
c2 = - 1
Since
The lines are intersecting.
The system of given equations have a unique solution.