Question

I'm solving using a substitution but it doesn't make sense, can someone help me?
2x+2y=38
y=x+3

Answer 1

\[2x+2(y)=38\]\[(y)=x+3 \]
\[2x+2(x+3)=38\]

Answer 2

\(\large\color{slate}{ 2x+2y=38 }\)
\(\large\color{slate}{ y=x+3 }\)

see the part, I am labeling in red, \(\large\color{slate}{ \color{red}{x+3} }\) ?
(according to your first equation) it is equivalent to \(\large\color{slate}{ y }\)

So this is what we do to the first equation:
\(\large\color{slate}{ 2x+2y=38 }\)

substitution:
\(\large\color{slate}{ 2x+2(\color{red}{x+3} )=38 }\)

Answer 3

like this. Makes sense?

Answer 4

After the substitution is plugged in, do I sole it then?

Answer 5

Find what x is. Then once you know what x is, plug it back in to either equation, and you can find what y is.

Answer 6

*solve

Answer 7

Yeah, once you solve for x, you can solve for y by plugging x back into either equation, and simplifying the algebra.

Answer 8

I got 8 for x.

Answer 9

x = 8 is correct

Answer 10

Can you find y?

Answer 11

I solve y the same way I solved x?

Answer 12

You could do that I suppose

Answer 13

11?

Answer 14

Yes. A short way to find y is:
You know x is 8.
You also know y=x+3, or y is 3 greater than 8.
So y is equal to 11

Answer 15

So my answer would be:
x=8
y=11

Answer 16

Yes

Answer 17

Thanks.

Answer 18

You can plug it in to either equation to check

Answer 19

2(8)+2(11)=38

Answer 20

I was stuck when finding y because the equation was already set I didn't know if should start over and find y or just leave it how it was to find y.

Answer 21

You could do both

Answer 22

Start with:
2x+2y=38
y=x+3
You know how to find x from earlier.
You can use the same method to find y, you just have to rearrange the second equation to become y-3=x

Answer 23

2(x)+2y=38
and
y-3=(x)

Combine.
2(y-3)+2y=38
And you can find y