the sum of two numbers is 31. The first is 5 less than the second. Find the numbers.

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OpenStudy (shadowfiend):

Can you convert this into an equation?

OpenStudy (anonymous):

x=5-y ??

OpenStudy (shadowfiend):

Not quite, it's \(x = y - 5\) (making \(y\) 5 less than \(x\)).

OpenStudy (shadowfiend):

So that's the first part, what about the part where it says that `the sum of two numbers is 31'. Can you make that into an equation?

OpenStudy (anonymous):

x+y=31

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OpenStudy (shadowfiend):

Right. So now you have two equations:
\[\begin{align}
x + y &= 31\\
y - 5 &= x
\end{align}\]

OpenStudy (shadowfiend):

Can you solve that system of equations?

OpenStudy (anonymous):

y-5+y

OpenStudy (anonymous):

=31

OpenStudy (shadowfiend):

Right, and then can you solve that equation for y?

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OpenStudy (anonymous):

that is where i am a little confused. do i minus a y?

OpenStudy (anonymous):

4y?

OpenStudy (shadowfiend):

So you have:
y - 5 + y = 31
You can put the ys together:
y + y - 5 = 31
Which is the same as:
2y - 5 = 31

OpenStudy (anonymous):

2y=26?

OpenStudy (shadowfiend):

Not quite, remember that if we want to move the 5 over to the right, you have to add 5 to both sides to cancel it on the left:
2y - 5 + 5 = 31 + 5
2y = 36

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OpenStudy (anonymous):

oh so i have to add 5 to equal it out since it is negative?

OpenStudy (shadowfiend):

Exactly.

OpenStudy (anonymous):

thats where i went wrong. y=18?

OpenStudy (shadowfiend):

Exactly.

OpenStudy (shadowfiend):

And then what's x?

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