Question

solve by elmination or substitution 7x+9y=17, 6y+9x=23

Answer 1

Have you chosen a method?

Answer 2

I was trying to use elimination but I can not figure out how to do it

Answer 3

Subtract one equation from the other, eliminating on variable each time.
7x+9y=17
9x+6y=23

In order to eliminate a variable you have to reduce it to zero, meaning that the two values must be equal. So the easiest one to start with is 'y', what could you do to make both of those the same number?

Answer 4

Well I tried multipying equation 1 by 6 and equation 2 by -9

Answer 5

While that would work, though your numbers could be smaller, when you subtract a negative number you are actually adding it. What is the smallest number that 6 and 9 will go into?

Answer 6

18

Answer 7

Right, so multiply (1) by 2 and (2) by 3:

(2)7x+9y=17 => 14x+18y=34
(3)9x+6y=23 => 27x+18y=69

Answer 8

but one has to be negative so they cancel right?

Answer 9

Yes, so now you can subtract one from the other.
27x+18y=69
-(14x+18y=34)
-------------
13x+0y=35

Answer 10

and then would i have to devide by 13

Answer 11

Yes, to solve for x

Answer 12

but that is the part I get confused at because it doesnt go in evenly so do I leave it as a fraction

Answer 13

Each instructor is different, some will ask that you reduce it to a decimal and some will insist you leave it as a reduced fraction. Most of the time these problems are designed to cancel out so I would just leave it for now and plug in to solve for 'y'.

Answer 14

My instructor hates decimals so I think I will leave it. Then I have to plug the fraction in to solve for y?

Answer 15

Yep.

Answer 16

Ok I think I got it thank you!

Answer 17

You're welcome.