Show that the paths represented by the equations x - 3y = 2 and - 2x + 6y = 5 are parallel.

Question

Philoid · Accepted Answer

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.