Show that the paths represented by the equations x - 3y = 2 and - 2x + 6y = 5 are parallel.
Given: x - 3y = 2 and - 2x + 6y = 5
To Prove: The paths represented by the given equations are parallel.
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 = - 3, c1 = - 2; a2 = - 2, b2 = 6, c2 = - 5
Since
Both lines are parallel to each other.