## ValentinaT 2 years ago Solving systems by substitution and elimination?

1. ValentinaT

$y = \frac{ 1 }{ 2 }x - 6$ 2x + 6y = 19

2. ValentinaT

I know that answer is (11, -1/2) but I don't know how to solve it.

So, you know what y equals. If you see y in another equation can't you just plug it in?

4. ValentinaT

What I meant is that, someone told me the answer, but not how they got it. Could you explain to me how they would have got (11, -1/2) as the answer?

I will ask you a series of questions to help you solve this. Question 1: what does y equal?

6. ValentinaT

-1/2

Y does not equal -1/2 Read the first equation out loud and listen to what y is equal to.

8. ValentinaT

1/2 - 6

If x = 25r + 25b Then x is equal twenty-five r plus twenty-five b.

10. ValentinaT

Okay.

Y = 1/2X - 6 There is no other answer. By writing y=1/2x-6 We say Y is equal to one half of x minus 6. There is nothing else that is the answer.

Question 2: If x = 5, what is y , if: x + 10 = y

13. ValentinaT

x plus ten.

This is the substitution part, if you know that x is 5..... What is y?

Y would then be x+10=y 5+10=y 15=y

16. ValentinaT

Okay.

Now that's just a basic use of substitution. Let's go back to your problem(s) You know what y is equal to y=1/2x-6 So then you look at the other equation 2x + 6y = 19 and say Well if i know what y is, I can replace it with the y there. So 2x + 6y = 19 turns into 2x + 6(1/2x - 6) = 19

18. ValentinaT

Okay.

So there's the way to solve for x. Once you get a numerical answer for x, you can solve for y.

20. ValentinaT

Okay, so what do you do afterwards?

Did you solve for x?

22. ValentinaT

Well, what I meant was do i combine 2x and 1/2x?

You need to distribute the 6 since it was 6y and then you can proceed with solving for x from there.

24. ValentinaT

5x - 36 = 19 5x = 55 x = 11 Replace x in one of the equations. y = 1/2(11) - 6 y = 5.5 - 6 y = -1/2

And you have just solved by substitution.

26. ValentinaT

How do you go from 2x + 6(1/2x - 6) = 19 to 5x - 36 = 19?

6 times 1/2x equals 3x and -6 times 6 equals -36 You may need to go back and review some algebra. It would help tremendously and I do not see another way for you to continue in mathematics without it.

I am going to link you to some pages. Please study them and use them and I suggest understanding these concepts before continuing your homeworkl.

29. ValentinaT

I've done the other problems myself, its just that i didn't understand this one.

30. ValentinaT

*I

Distribution property is one of the earliest rules learned in algebra. If you can get from 2x + 6(1/2x-6) = 19 to 5x-36=19 well then there may be some necessary review:

33. ValentinaT

Thank you.

34. ValentinaT

What do you want?

35. ValentinaT

I blocked you?

36. ValentinaT

It doesn't say I did.

37. ValentinaT

It doesn't say I blocked you. I have to go.

38. mustry

where?

39. mustry

Valentina?