## anonymous 4 years ago Solve using the elimination method 7x + 7y = 7 x + 2y = 2 pleas explain I do not get this at all

1. Akshay_Budhkar

ok let us go step by step

2. anonymous

step one is do divide the first equation by 7 to make your life simpler. you get $x+y=1$ and now i shut up

3. Akshay_Budhkar

$7x + 7y- 7 \therefore x+y =1 \therefore x=y-1$

4. precal

7x+7y=7 x+2y=2 The goal is to eliminate the x's or the y's It is your choice

5. precal

or you could mutiply -7 to the second equation

6. anonymous

ok now i put in my two cents again. says "elimination" not "substitution" although i would use the second method as well

7. precal

Technically the method does not matter but since it did say elimination it is better to cancel out the x's or the y's I am choosing to get rid of the x's by multiplying -7 to equation 2

8. Akshay_Budhkar

substituting that in equation 2 we have$\begin {array} x x+2y=2 \\ y-1+2y=2 \\ 3y=3 \\ y=1 \end {array}$

9. Akshay_Budhkar

10. Akshay_Budhkar

11. Akshay_Budhkar

ok in this you can solve by subtracting the two equations that is x+y=1 and x+2y=2.. you get 2y-y=2-1 therefore y=1

12. anonymous

ok I am so confused

13. anonymous

ok I get it sorry didnt get it at first

14. Akshay_Budhkar

so is it fine now?

15. anonymous

Yes it is thank you so much I get it now i hope

16. Akshay_Budhkar

if u have any doubt clear it =D all the best

17. anonymous

Thank you :)

18. anonymous

I thought it would be 2y-y=2/1

19. anonymous

there for y=2

20. precal

I will do it for you using elimination

21. anonymous

i just need the process explained to me it just is not clicking im sorry

22. precal

7x+7y=7 x+2y=2 7x+7y=7 -7(x+2y=2) 7x+7y=7 -7x-14y=-14 add equations together -7y=-7 divide by -7 to both sides y=1 x+2y=2 x+2(1)=2 x+2=2 -2 both sides x=0 solution x=0 and y=1

23. anonymous

ok this makes since to me thank you

24. anonymous

so this would be and infanite solution correct because it would graph as the same line not two intersecting line?

25. precal

Another name for this method is called multiplication and addition method First you pick a number to multiply one of the equations then you add both equations together goal is to get rid of the x's or the y's that is why is is called elimination. If you wanted to get rid of the the y's instead you would have to multiply 2 to the first equation and then -7 to the second equation this will produce 14y and -14y and then you would have solve for x first. Many ways to eliminate x's or y's

26. precal

No this is one solution because we were able to find the point of intersection

27. anonymous

oh ok so what would a infanite solution look like?

28. anonymous

sorry to ask so many questions, but I really want to grasp this and I am having a really hard time

29. precal

infinite solutions is the same line given in multiple form example x+y=4 2x+2y=8 did you notice they are the same I only multiply 2 to the original equation

30. anonymous

yes I see

31. precal

No solution is 2 parallel lines, they never cross. look for same slopes y=2x+3 y=2x+6

32. anonymous

thank you so much for explaining this I understand it so much better now than i did from the book

33. precal

The number of solutions is determined by the number of times the equations cross: One solution means they cross in one place (X,Y) No solution means they do not cross (Parallel lines) Infinitely many solution means they cross in many places (because they are the same line)

34. anonymous

Thank you so much

35. precal

Anytime :)