## anonymous 5 years ago Could someone please show me how to solve the system by elimination method? 5x+3y=-7 7x-2y=13

1. anonymous

Certainly. The elimination method allows you to form a new equation with only one of your variables by adding a multiple of one equation to another. First pick a variable you want to get rid of.

2. anonymous

Could you show me how this is done step by step?

3. anonymous

Yes, pick a variable you'd like to eliminate (x or y).

4. anonymous

x

5. anonymous

Ok, so checking the coefficients on x in both equations, we can see that if we multiply the first equation by $$\frac{-7}{5}$$ We will have a -7 coefficient on our x term. So rewrite the first equation after multiplying it by $$\frac{-7}{5}$$

6. anonymous

If anything I say doesn't make sense, stop me and let me know.

7. anonymous

ok

8. anonymous

So what do you get when you multiply the first equation by $$\frac{-7}{5}$$.

9. anonymous

do you make the 55 a fraction then cross multiply

10. anonymous

No, multiply both sides of the whole equation by -7/5

11. anonymous

$\frac{-7}{5}(5x+3) = \frac{-7}{5}(-7)$ And simplify.

12. anonymous

What do you get?

13. anonymous

While you're working it out I'm gonna grab some coffee.

14. anonymous

35+3 =-49

15. anonymous

You forgot to (a) change the signs (it was a -7) (b) put each of those over 5 (and simplify the 35) (c) keep your x.

16. anonymous

It should be: $\frac{-7}{5}(5x + 3y) = \frac{-7}{5}(-7)$ $\frac{-7}{5}(5x) + \frac{-7}{5}(3y) = \frac{49}{5}$ $-7x - \frac{21}{5}y = \frac{49}{5}$

17. anonymous

Right?

18. anonymous

yes

19. anonymous

Ok, now add this equation to the other one. $$7x\ - 2y = 13$$ + $$-7x - (21/5)y = 49/5$$ ============== For now don't bother to try to combine the fractions and non-fractions, just eliminate the x.

20. anonymous

ok

21. anonymous

What do you get for the new equation that only has y's?

22. anonymous

13/7(7x+2y)=13/7(13)

23. anonymous

is this step right

24. anonymous

No. Just add the two equations from top to bottom: $$7x \ - 2y$$ = 13 + $$-7x - (21/5)y = 49/5$$ =============== $$0x - 2y - (21/5)y$$ = 13 + 49/5

25. anonymous

oh ok

26. anonymous

Now multiply that whole equation by 5 to get rid of the fraction

27. anonymous

What do you get?

28. anonymous

The equation on the bottom that only has y's that is.

29. anonymous

so if i multiply all by 5 I get 10y -10=65+245

30. anonymous

No. 5*(-2y) = -10y 5*(-21/5)y = -21y 5*13 = 65 (this part you did correctly) 5*49/5 = 49 So the equation would be -10y -21y = 65 + 49

31. anonymous

32. anonymous

-31y=114

33. anonymous

Right, and now y =?

34. anonymous

Just leave it as a fraction.

35. anonymous

-31/114

36. anonymous

Yep. Now plug that in for y into either one of your original equations and solve for x.

37. anonymous

Err wait, no. It's -114/31

38. anonymous

You need to practice your distribution rules, and working with equations. I suggest http://www.khanacademy.org/video/solving-equations-with-the-distributive-property?playlist=Algebra%20I%20Worked%20Examples

39. anonymous

thank you

40. anonymous

Of course! =)

41. amistre64