Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets.
4x - 3y = 6
-12x + 9y = -24

- anonymous

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- schrodinger

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- anonymous

@JoannaBlackwelder

- anonymous

how do i solve this one

- anonymous

is it like the last one we did

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## More answers

- JoannaBlackwelder

It says you can use any method. Do you have a preference?

- anonymous

i dont lol

- JoannaBlackwelder

No, it is not a partial fraction decomp.

- JoannaBlackwelder

I like the addition method. Let's use that.

- anonymous

ok

- JoannaBlackwelder

So, we need to make the equations so one variable cancels.

- JoannaBlackwelder

When we add them

- JoannaBlackwelder

|dw:1439920308781:dw|

- anonymous

ok

- anonymous

so do we cancel out the y or xes first

- JoannaBlackwelder

Either is fine. What do we need to do to cancel the x's?

- anonymous

add them together

- anonymous

these are my answer

##### 1 Attachment

- JoannaBlackwelder

Ok, if we just add them together directly we get:

- JoannaBlackwelder

|dw:1439920522907:dw|

- anonymous

haha i just got that

- anonymous

like the same time you diid but you posted it first

- JoannaBlackwelder

Ok, but that doesn't cancel out either variable.

- JoannaBlackwelder

So, we need to multiply up the equations so that when we add them, one of the variables cancels.

- anonymous

ok so how do we do that

- JoannaBlackwelder

|dw:1439920656644:dw|

- anonymous

ok i still dont fully comprhend what you did there

- anonymous

@JoannaBlackwelder

- JoannaBlackwelder

I took the first equation and multiplied it by 4 so that the coefficients of the x terms are equal but opposite signs.

- anonymous

ohh ok makes sence

- anonymous

so is my answer c

- anonymous

@JoannaBlackwelder

- anonymous

@isaac4321

- JoannaBlackwelder

No, we need to add the equations together now.|dw:1439921457921:dw|

- JoannaBlackwelder

Both variables end up canceling out. And what is left over is not a true statement since 0 does not in fact equal -6

- JoannaBlackwelder

When that happens, the equations have no solution.

- anonymous

well umm my answer dont have that as a thing to choose

- JoannaBlackwelder

D is the notation for no solution

- anonymous

ohh i knew that lol

- JoannaBlackwelder

No worries :-)

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