Question

Not sure what closed meant, thought it was to inform other people I've been helped already :\

Answer 1

you have to find what 2 times X subtracted by 3 times Y =16
so try a few numbers like 2 for X and 4 for Y

Answer 2

i hope that helped you

Answer 3

pretty confused

Answer 4

yea it is

Answer 5

have you learned the elimination method yet?

Answer 6

Unfortunately can't say I have

Answer 7

well, it's fairly easy and would be really nice for this problem. you down for giving it a go?

Answer 8

First you have to set up the equations, i think the easiest way is substitution.
\[2x-3y=16 \]\[-3x+2y=-19\]
You then do 2-3x which gives you -1x after that you move to the next set. -3y+2y which gives you -1y. Then you move past the equal signs and do 16-19 which gives you -3. at this point you should have \[-1x-1y=-3\]
now you want an equation for substitution. so you get x by itself. add 1x to both sides. so you are left with \[-1y=1x-3\]
after that you still want y by itself so divide -1 with everything. you should then get
\[y=-x+3\]
now that you have this equation you can go back to either set of inequalites. i chose the first set. So think of the y equation as a number. now you are going to have
\[2x-3 (-x+3)=16\]
after distributing you should have
\[2x+3x-9=16\]
now combine like terms and you should have
\[5x-9=16\]
now you add 9 to both sides and get
\[5x=25\]
divide 5 by both sides and x=5
now to get Y you just plug in your x (5) into one of the equations from the beginning. i chose the first one again. so you do
\[2(5)-3y=16\]
you then get
\[10-3y=16\]
subtract 10 from both sides and you should get
\[3y=6\]
divide three from both sides and your answer should be y=2
So x=5 and y=2

Answer 9

Wow, thought it was glitched and stuck on saying you were typing I really appreciated that NB. Pg, if you would like to explain it to me I'd love to try it out

Answer 10

May not be worth it though, I already gave nb the best answer. Don't want you to waste your time.

Answer 11

no problem, glad i could help

Answer 12

elimination is the process of "eliminating" variables from the equations in a systematic way.

let's say we wanted to eliminate the x variable from the equations. we'll do this by getting the coefficients of the x terms to be opposites of each other by multiplying one or more of the equations:

2x - 3y = 16 is the same as 3(2x - 3y = 16) => 6x - 9y = 48

-3x + 2y = -19 is the same as 2(-3x + 2y = -19) => -6x +4y = -38

now we can add the equations. I know it seems a bit weird but it's all valid.

6x - 9y = 48
-6x + 4y = -38
___________________
-5y = 10

=> y = -2.


We can either substitute back into one of the equations and solve for x or we can eliminate y and see what we get for x. I'll eliminate again to demonstrate the method but it's also very helpful if you get a fraction in your solution...

2x - 3y = 16 is the same as 2(2x - 3y = 16) => 4x - 6y = 32

-3x + 2y = -19 is the same as 3(-3x + 2y = -19) => -9x +6y = -57

now we can add the equations.

4x - 6y = 32
-9x + 6y = -57
___________________
-5x = -25

=> x = 5.

Answer 13

so the soultion is the point (5, -2). and you can check that it satisfies both lines.

Answer 14

it's all about the learning... not the points.

Answer 15

Wow pgpilot had no idea about that. Would you rather use that method over substitution? Thanks for taking time to explain that.

Answer 16

i like it better than substitution. you're welcome1