Question

What is the correct classification of the system of equations below?


2x + 6y = 8
y - 2x = 2

A. parallel B. coincident C. intersecting

Answer 1

The general form of a straight line

If you have two equations:
ax+by=c
and
px+qy=r

AND If
a b c
-- = -- = --
p q r

then the two lines are coincident - that means they have INFINITE SOLUTIONS.

If
a b c
-- = -- =/= -- ....{"=/=" means 'unequal to')
p q r

then, the lines are parallel, and they have NO SOLUTIONS.

If
a b
-- =/= --
p q

then the lines are intersecting, and they have ONE UNIQUE SOLUTION.

compare and check out what's the case for your question.