1. ## System of equations

I am working on system of equations, and I am totally lost, every time I do it it turns out really wrong. Could some one help explain this to me.

Find the vaules of x and y that solve the following systems of equations:

-7x+9y=-2
-3x+2y=1

Thanks!

2. Originally Posted by GeinoD
I am working on system of equations, and I am totally lost, every time I do it it turns out really wrong. Could some one help explain this to me.

Find the vaules of x and y that solve the following systems of equations:

-7x+9y=-2
-3x+2y=1

Thanks!
there are two main ways to do problems like these. there is elimination and substitution. i will describe elimination, since it is generally what i prefer to do

first we want to get the coefficient of one of the variable the same in magnitude in both equations. then we can add or subtract one equation from another (depending on signs) to eliminate that variable. once we get rid of that variable, only one of the variables are left which we can easily solve for. we solve for it, and then use it to find the other variable that we eliminated originally.

let's say we want to eliminate the x's

first step, multiply equation (1) by 3, and equation (2) by -7

what to you get?

3. I'm Sorry I think we are supposed to use Substitution to solve the system, if that sounds about right.

4. Originally Posted by GeinoD
I'm Sorry I think we are supposed to use Substitution to solve the system, if that sounds about right.
...ok. in that case. solve for y from equation (2) and plug it into equation (1) so you can solve for x. then back-substitute to solve for y

5. This is what I did.

-3x+2y=1
+3x +3x
2y=3x+1
/2 /2 /2
y=3/2x+1/2

-7x+9(3/2x+1/2)=-2

this is where I get into trouble...

-7x+27/2x+9/2=-2

At this point I think I am way off.

6. -7x+27/2x+9/2=-2

-7x+27/2x+18

13/2x=-20
x=53/2

7. Originally Posted by GeinoD
This is what I did.

-3x+2y=1
+3x +3x
2y=3x+1
/2 /2 /2
y=3/2x+1/2

-7x+9(3/2x+1/2)=-2

this is where I get into trouble...

-7x+27/2x+9/2=-2

At this point I think I am way off.
no, you're right so far. continue. solve for x now

8. Originally Posted by GeinoD
-7x+27/2x+9/2=-2

-7x+27/2x+18

13/2x=-20
x=53/2

9. -3x+2y=1
+3x +3x
2y=3x+1
/2 /2 /2
y=3/2x+1/2

-7x+9(3/2x+1/2)=-2

-7x+27/2x+9/2=-2

-7/1x+27/2+9/2=-2

-14/2x+27/2x+9/2=-2

-13/2x+9/2=-2

9/2 9/2

-13/2x=9
-13/2 -13/2

x=18/13

10. When I put 18/13 in place of x in the next equation I end up with y=312/13

11. Originally Posted by GeinoD
-3x+2y=1
+3x +3x
2y=3x+1
/2 /2 /2
y=3/2x+1/2

-7x+9(3/2x+1/2)=-2

-7x+27/2x+9/2=-2

-7/1x+27/2+9/2=-2

-14/2x+27/2x+9/2=-2

-13/2x+9/2=-2

9/2 9/2

-13/2x=9
-13/2 -13/2

x=18/13
Originally Posted by GeinoD
When I put 18/13 in place of x in the next equation I end up with y=312/13
you need to review how to solve equations. your solution is again wrong. the correct answer is: x = -1. now use that to find y

(you can check your answer you know. when you got x = 18/13, why didn't you plug it into the left hand side of the (red) equation and see if you actually got -2 as the answer?)

12. So is the red one where I went wrong?

13. anyone? I'm totally freaking out because at this rate it will take me 3 days to finish. What am I doing wrong, I just dont get it and there is no one I can ask for help from

14. Originally Posted by GeinoD
So is the red one where I went wrong?
no. that's not where you went wrong. it is the line you should have checked your answer in

you went wrong 3 lines after that. you should have subtracted 9/2 from both sides, but you did something else, i'm not even sure what

-7x+9y=-2
-3x+2y=1

3(-7x+9y)=-2*3
-21x+27y=-6

7(-3x+2y)=1*7
-21x+14y=7

-42x+41y=1

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