## InsanelyChaotic 3 years ago Would anyone be so gracious as to helping me get a better understanding of the dreadful algebra!??!?!!? :) Explain, in complete sentences, how you would use the elimination method to solve the following system of equations. Provide the solution to the system. 2x + 9y = 4 3x + 7y = -7

1. Venomblast

1st you want to figure out which variable you want to solve

2. InsanelyChaotic

X

3. Venomblast

ok. oh n btw i replied. the answer is A!!! fromt he previous question

4. InsanelyChaotic

thank you love!!!! :)))))))))))) I got that answer after I "closed" the question box

5. Venomblast

i said it 2 times. lol anywayz let do this problem

6. InsanelyChaotic

thank you nonetheless! ok let's go!

7. terenzreignz

Hey, an intermission, if you would oblige me... if x = y, then ax = ay right?

8. terenzreignz

And if a = b and c = d then a + c = b + d Don't worry, these are relevant, we'll use them.

9. InsanelyChaotic

Thank you kind sir....! @terenzreignz

10. Venomblast

man i hate the ax=ay method

11. terenzreignz

So you have 2x + 9y = 4 From our first rule, we can get 7(2x + 9y) = 7(4) 14x + 63y = 28, let's stop here, and call this "equation 1" You also have 3x + 7y = -7 Again, from our first rule, we can get -9(3x + 7y) = -9(-7) -27x - 63y = 63, stop here again, call this "equation 2" Are you getting it so far?

12. InsanelyChaotic

Yes, I've gone thru this a time before! But one question, how did you get the "7" in 7(2x+9y)

13. InsanelyChaotic

If you don't mind me asking.....! :))

14. InsanelyChaotic

Here's a joke: Subway called, they want their 6 inch back ;)

15. Venomblast

LOL

16. InsanelyChaotic

Another joke/flattery I made up: Verizon called, they want their "SMART" phone back

17. terenzreignz

Ok... You said you wanted to solve for x first (personally, I'd have gone for y first) So, we have to somehow get rid of the y. To do that, you have to make it so that the coefficient (the number that goes beside the letter) of the y in the first equation is equal to the NEGATIVE of the coefficient of the y in the second equation. In the first equation, the coeff of y was "9" and in the second, it was "7" You need to get what's called their "least common multiple" And that's 63. 63/9 is 7, so that's what I multiply to the first equation. 63/7 is 9, so that's what I multiply to the second equation, and then I NEGATED it (multiplied it by -1)

18. terenzreignz

You'll see why this is done, when I proceed... shall I?

19. Venomblast

20. InsanelyChaotic

oh my god....this is actually making sense!!!!! :')

21. terenzreignz

Remember our second rule? if a=b and c=d then a+c = b+d ? We'll just apply that, on a larger scale, sort of...

22. InsanelyChaotic

I remember! I will, I promise!

23. terenzreignz

All right, equation 1: 14x + 63y = 28 equation 2: -27x - 63y = 63 Remember these?

24. InsanelyChaotic

I do, yes

25. terenzreignz

Now we use the second rule, we add both expressions on the left, and equate them to the sum of the expressions on the right: 14x + 63y - 27x - 63y = 28 + 63

26. terenzreignz

Notice something?

27. Venomblast

combine like term *cough**cough*

28. InsanelyChaotic

I'm writing down the steps to refer to, but yes, I notice that in order to prolong the steps, I'll have to combine

29. terenzreignz

and...?

30. InsanelyChaotic

Get x by itself

31. terenzreignz

And then you'll have reduced it to a linear equation in one variable. Solve for x, and you're almost done! Just substitute that x which you get for the x in either one of the equations you started with, and then solve for y, and then you'll be done!

32. InsanelyChaotic

33. terenzreignz

I appreciate your appreciation; have fun! :)

34. InsanelyChaotic

I will never have fun with math, but thank you:)