Question

The difference of two numbers, a and b, is 21. The difference of 5 times a and two times b is 18. What are the values of a and b?
4, 1
-19, 40
20, 1
30, 9
-8, -29

Answer 1

Do you know the method of elimination, or the method of substitution when you have 2 equations? Your 2 equations are:

a - b = 21
5a - 2b = 18

Answer 2

i forgot

Answer 3

Here's substitution for example. You know that the a and b must be the same in both equations. So if you can rearrange one equation to get "a" by itself, then all you have to do is plug in the "new a" to the second equation

Answer 4

a-b = 21. You can rearrange this fairly easily by bringing the b over. You get a = 21 + b. Now you can plug in "21 + b" where the "a" is in the second equation, and solve for b. Does that make sense?

Answer 5

no @fission-mailed but thanks for helping

Answer 6

You want to figure out what "a" and "b" are. Right now you have equations with 2 variables in them. You can't solve them as they are in that form at this level, so you want an equation that has only one, which you DO know how to solve.

a-b = 21. But a and b could be anything. If you knew a, would you know how to solve for b?

Answer 7

yea @fission-mailed

Answer 8

So if you can change one of the equations so that it's written as "a = ..." or just "b= ...", then you have figured out a NEW way to write that variable, but you don't yet know what it actually equals. Then you can just look at the second equation, and replace the ugly old variable with your new way of writing it.

What you will end up with is an equation with only one variable. These you know how to solve. Is that making more sense?

Answer 9

is a=-21 and b = -24/5

Answer 10

@fission-mailed

Answer 11

If a = 21 + b, then you can rewrite 5a - 2b = 18 as this:
5(21+b) - 2b = 18

You basically just replace where the "a" was with "21 + b". Now you have just b's. Expand and solve:

105 + 5b - 2b = 18
Collect like terms:
3b = 18 - 105
3b = -87
b = -29

Answer 12

So now you have b = -29. To find the other value, just plug in "-29" to either one of the equations to get the the a. We could just use the first equation because it's easier. But either one will give you the same answer.

a - b = 21
a - (-29) = 21

Then just solve for a to get a. Now you have a and you have b, so you have the answer. Is there anything that you're still unclear on?

Answer 13

-8

Answer 14

@fission-mailed

Answer 15

Correct :) Do you understand, or is there anything else I need to explain more clearly?

Answer 16

i understand