Help with solving system equations using elimination?

Question

2x+3y=1
4x+6y=2

2x-4y=5
2x-4y=6

Could u explain how u got the answer. Thanks in advance.

Answer 1

2x+3y=1......(1)
4x+6y=2......(2)
2*(1):4x+6y = 2......(3)
Since (2) and (3) are exactly the same, you have infinitive number of solutions: [x, (1/3)(1-2x)]

2x-4y=5
2x-4y=6
The two equations represent two parallel lines. Therefore, there is no solution. The system is inconsistent.

Answer 2

In both cases there -is- no unique solution.
In the first case, the lines described are, in fact, the -same- line and so there are an infinite number of solutions.
In the 2'nd case, the lines described are parallel and never cross so there is -no- solution.

Doug