The Substitution Method "solve for the indicated quantities"

[hauservi]

Ok, I hope I do this right...

The problem says
Set up a system of lineral equations and solve for the indicated quantinties.

Two positive numbers have a difference of 8. The larger number is 2 less than 3 times the smaller number. Find the numbers.

I have tried to say... a+b=-8 and 3b-2a=8 and then solve for b so I can substitute it in the 2nd equation...

b= -a-8

2nd equation would then be

3(-a-8) - 2a = 8

Then I solve for a. But I am doing something wrong because I get a= -6.4

The numbers are 13 and 5 but I can't come up with the right equations

[stapel_eliz]

Set up a system of lineral equations and solve for the indicated quantinties.

Two positive numbers have a difference of 8. The larger number is 2 less than 3 times the smaller number. Find the numbers.

I have tried to say... a+b=-8 and 3b-2a=8 and then solve for b so I can substitute it in the 2nd equation...

Let's start by setting up expressions for the various listed quantities and relationships:

. . . . .smaller number: a
. . . . .larger number: b

. . . . .difference: b - a = 8

. . . . .three times smaller: 3a
. . . . .larger: b

. . . . .(larger) is (three times smaller) less (two): b = 3a - 2

See what you get!

[hauservi]

THANK YOU! That has been driving me nuts for DAYS