Question

A first number plus twice a second number is 24. Twice the first number plus the second number is 21. What are the numbers?

Answer 1

x+2y=24 is going to be the equation for the first one....

Answer 2

Can you try to find the second one?

Answer 3

y+2x=21

Answer 4

=24*

Answer 5

but I would word it to where the x term comes first so it is easier :)

Answer 6

oh I typed my first one in wrong, it is actually 21

Answer 7

oh okay :)

Answer 8

Correct, and

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Answer 9

Are they both 21 or is one of them 24 still?

Answer 10

One of them is 24
I edited the original question and fixed it.

Answer 11

okay great! So now that we have both:
x+2y=24
2x+y=21

We can now substitute to find the values of x and y :) I can show you the steps if you want?

Answer 12

Ok,
I tried a lot of the different combinations of numbers that fit for the first one, but none of them worked for the second one, they were all way too big.

Answer 13

Substitution is not where you replace numbers into x and y, but rather one equation into the other. So first, we need to isolate x for the first one.

Answer 14

Ok so x=24-2y?

Answer 15

Correct! So now that we have that, we can then plug it into the x of the second equation like so:

2(-2y+24)+y=21

Then you need to distribute the 2 to the -2y and 24.

Answer 16

Do you understand what I did there?

Answer 17

-4y+48+y=21

Answer 18

Correct! Then you need to combine like terms.

Answer 19

which can be simplified to -3y=-27

Answer 20

Correct! Then divide both sides by -3

Answer 21

so y=9

Answer 22

so put that into the next equation to solve for x

Answer 23

Yes. Then you can replace y=9 into either one of the equations (It doesn't matter which) and solve

Answer 24

It would be easier to put it into the x=-2y+24 since x is already isolated

Answer 25

x+18=24, so x equals 6!

Answer 26

Thank you so much for the help! :) :)

Answer 27

Yes! Great job! So:
y=9
x=6

And that's all! :D

Answer 28

No problem!

Answer 29

Would you mind hitting the 'close' button to close this question? Thank you!

Answer 30

Ok

Answer 31

Thank you!