Question

GRAPH ATTACHED!

The graph shows the system 3x + 6y = 18 and x + 2y = 6. What is the solution for the system?

A. one solution
B. no solution
C. infinitely many solutions
D. cannot be determined

Answer 1

Divide the first equation by three and you have the second equation.

Answer 2

Infinitely many solutions.

Answer 3

3x + 6y = 18 and x + 2y = 6

subtract 3 times the second equation from the first one

0 = 0

or: divide first equation by 3; they are the same equation.

Infinitely many solutions.

Answer 4

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.

check what is the case in your question.