ShmoopTube

00:03

Shmoopy-Doo, where are you?

00:07

Solve for y using substitution: 3x + 4y = 15 -2x + 6y = 12

00:15

And here are the potential answers...

00:23

OK so what is this question asking?

00:24

It's just another isolation and plugging problem.

00:27

We have to solve for y by getting rid of x.

00:30

to draw any undue attention.

00:30

Then we just solve for y as in any normal, one variable problem.

00:34

So let's take the first equation and rewrite to get 3x equals 15 minus 4y.

00:41

Now divide both sides by 3 and we have x equals 5 minus 4/3 y

00:48

Then we just substitute 5 minus four-thirds y inside of x in the next equation

00:57

and we get negative 2 times the quantity 5 minus four-thirds y...plus 6y equals 12.

01:07

We distribute the negative 2 to get negative 10 PLUS eight-thirds y plus 6y equals 12.

01:16

Simplify a bit more by rewriting as negative 10 plus 8y over 3 plus 18y over 3... because

01:23

6 can also be written as 18 over 3, which gives us common denominators... equals 12.

01:31

Dealing with just the fractions we get 18 plus 8 which is 26y... over 3.

01:36

Add 10 to both sides of the equation and we can simplify everything to 26 y over 3 equals 22.

01:43

Multiply both sides by 3 over 26, and we get y equals 66 over 26.

01:56

The greatest common factor of 66 and 26 is 2 so we can simplify this to 33 over 13.

02:03

So our correct answer for y is B.

02:05

As in, 'Burlap sack.'

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