MeganDarling 3 years ago Help please? :o 1. Solve the system by substitution- 2x+y=-11, 3x-4y=11. I'm so terrible at substitution and elimination >.< 2. Solve the system using elimination- 2x+6y=-12, 5x-5y=10. 3.What is the solution of the following system?-3x-2y=-12, 9x+6y=-9. Help with any of these would be greatly appreciated thanks.

1. MeganDarling

Even any tips on how to do these would be nice :/

2. joshi

ok so looking at the first one. basically you have to multiply one or both of the equations by a number so that the coefficient of one of the variables is the same so that when you subtract/add them then it will cancel. ^that sounds confusing, here's an ex for elimination: x+y=5, 2x+y = 30 so if we multiplied the first equation by 2, we'd get: 2x+2y=10 right? so we can subtract now... 2x+2y=10 - 2x+y=30 ------------ 0 + y = -20 ------------- and now we can plug in -20 for y back in the equation to find x. hope that made sense

3. MeganDarling

Yeah that made more sense than my textbook does haha. How about a substitution example? Or how you can tell if a system is dependant or independant? or has infinately many solutions?

4. joshi

haha yeah textbooks can be annoying sometimes. so substitution: x+y=2 x+4y = 7 so in substitution we basically just have to get any variable on its own so that we can substitute it into another equation. pretty much cause solving for 2 variables is hard. so i can get either x or y by itself from the 1st equation (or the second if you want). x+y = 2 so x+y-y = 2-y so, x+0=2-y or x=2-y now we know what x equals, so lets put it in the other equation. (x) +4y=7 OR (2-y) +4y = 7 [see what i did there? ] so 2-y+4y=7, 2+3y=7, 3y=5, y=5/3 and you can put this in the x equation (x=2-y) to get x aswell :)

5. MeganDarling

Very much so >.< Man that all still seems pretty confusing but I really appreciate the help! I always just tend to get one step wrong along the way and mess the whole thing up lol, It's in my nature :P

6. MeganDarling

x-y=11, -x+y=-11 Would one like this have infinitely many solutions?

7. joshi

same here. i used to hate math so much, i still sort of suck at it. even if i get the stuff i make little mistakes. <.< anyway, if you just practice it a bit i'm sure you'll get it. yeah that would have infinitely many solutions because they're the same equation just written differently. so on a graph, there would be just the one line. this might help: http://www.mathocean.com/2009/10/system-of-linear-equations-consistency.html

8. MeganDarling

Well I'll keep trying x.x I just need to do decently on my daily tests which so far I haven't really haha. And yeah that's what i though lol. Funny I swear I've been to that website before x)

9. joshi

daily tests? ai yi yi. haha well that's good, good luck!

10. MeganDarling

Yeah every day, about 10 question tests x.x it's ridiculous.. But thanks !

11. joshi

woah that is a little ridiculous. well you get practice from it i suppose. yeah no problem :D