confused on this one because if i multiply the first equation by 2, it cancels out both the x and y components.
Solve by the elimination method.
2x + 3y =1
4x + 6y = 2

- anonymous

- chestercat

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- anonymous

that is okay but you need to multiply first equation by -2

- anonymous

sorry about that...you will get 0=0 which is always true so infinitely many or all real numbers as solution

- anonymous

ok, that is the first time i saw the answer come out like that, thanks!

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## More answers

- anonymous

you're welcome....good job on elimination...you may also get something like -2=0 which is never true so NO SOLUTION

- anonymous

so which would it be, infinitely many solutions or no solution?

- anonymous

no solution is a different type-when left side doesn't equal right side INFINETLY MANY/ALL real numbers mean same things

- radar

You have what is known as an identity.

- anonymous

exactly radar

- radar

I hope the course that ms elegant prepared for such an event lol

- anonymous

can you help me with polynomial question Find polynomial P(n)=Sn for 1, 2, 3, ...10 and explain method

- anonymous

so the answer i get when multiplying by -2 is 0=-2. so I'm guessing that the answer is there is no solution.
but how do i perform a check to make sure that my answer is right?

- radar

It is unsolvable,it is an identity, it is the same equation just one is double the other you need two distinct equations for the two unknowns.

- radar

btm2011, I wouldn't be much help on that polymonial series!

- anonymous

ok, so there is no solution, thx!

- radar

Ms elegant do you understand even though they provided you with two equations, they are actually the same, one does not provide any new information for you.

- anonymous

for that problem the answer is all real numbers, infinitely many (identity) because 0=0
-2(2x+3y=1)____-4y-6y=-2

- anonymous

-4y-6y=-2 + 4x+6y=2

- anonymous

There is a solution!

- anonymous

ok i think i got it, there is a solution, but it is just an infinite amount of solutions that can be the answer, right?

- anonymous

YES...bc every number equals itself

- radar

yes, x=0 and y=1/3 could be a solution, but there is no specific solution, I could put down another solution like x=-2, y=1

- anonymous

ok, i get it. and that's the check, that several answers fit this equation - so there are infinite solutions, not just one

- radar

That is what it seems to be.

- anonymous

ok great thx! i appreciate the explanation so that i could understand what i was doing

- anonymous

GREAT!

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