## anonymous 5 years ago 5/4x+1/8x=5/8+x ?? I am so bad at fractions

1. anonymous

like this?: $\frac{5}{4}x+\frac{1}{8}x=\frac{5}{8}+x$

2. anonymous

yes but how do you solve it??

3. anonymous

ok, multiply everything by 8: 10x+x=5+8x 3x=5 x=5/3

4. anonymous

ok

5. anonymous

why do we multiply itby 8 b/c it is the common denominator?

6. anonymous

its the least common multiple of the denominators, so it gets rid of all the fractions.

7. anonymous

ok I will kepp that in mind thank you..

8. anonymous

you're welcome

9. anonymous

do you k now anything about the elimination method?

10. anonymous

do you have a specific problem?

11. anonymous

just getting it to opposite and yes! the 5x+6y=2 10x+12y=4

12. anonymous

well those equations are multiples of each other

13. anonymous

so elimination isnt really useful here

14. anonymous

that answer calls for use of the elimination

15. anonymous

to eliminate either x or y you multiply the first equation by -2, then add. But then you get 0=0

16. anonymous

there are actually many solutions to that system

17. anonymous

theyre both the same equation

18. anonymous

there is an option for no solutions or many solutions

19. anonymous

so many solutions woiuld fit

20. anonymous

there are many solutions, because theyre both the same equation so you can pick any x and find a corresponding y to make the equation true

21. anonymous

thank you again

22. anonymous

but something like 2x+3y=15 4x+y=20 you would multiply the first equation by -2 and then add them together to eliminate x -4x-6y=-30 4x+y=20 -5y=-10 y=2 then plug back in to find x 2x+6=15 x=9/2

23. anonymous

then the solution is unique