Better way to solve this math problem...?

Question

Please, help me with it! I was out on the day that my class discussed how to solve these problems, and I think that I'm doing it the long way. I really need help!

The sum of two numbers is 90. Their difference is 18. Find the numbers.

What I have been doing is finding two equations:
x+y=90
x-y=18

Solving for one variable:
x=y+18

Substituting for that variable:
y+18=90

And going on to solve.

I know there's got to be a better way to do this. Please show me how to work this problem in a more efficient way so my homework won't take me hours!

Answer 1

Read ahead in your book one section. There is something called elimination. Some books teach how to do substitution first because you can technicallly solve anything with it.

Answer 2

Yes, there is a better way. You can add left sides and right sides of the system of equations. There is a rule in math that says you can do it like that.

If you add them, it will be:
x+y+x+(-y) = 90+18
Now you can solve for x. Once you obtain a value for x you can use it in any of the two equation to obtain y.
I'm delibarately not finishing up the problem :-) because that would be insulting your intelligence.

Answer 3

x - y = 18 ==> x = y + 18

x + y = 90
(y + 18) + y = 90
2y = 72
y = 36

x + y = 90
x + 36 = 90
x = 90 - 36
x = 54

Answer 4

how about 2y+18=90

y + (y+18)=90

Answer 5

yes, you're working way too hard. you can find it by doing it all in 1 problem.
x + (x -18) = 90

Answer 6

x+y=90
x-y=18
adding together
2x=108
x=54
y=x-18=36

Answer 7

x + (x-18) = 90
Simplify and solve.

Answer 8

Nope, there isn't a better way. You're doing it the easiest way possible. =)

Answer 9

That's right.

Answer 10

i'm confuse.