SOLUTION: Solving systems of equations, use either substitution or elimination method. The problem I have is: 1/2x - 7/5y = -1 1/3 x + y = 9 My teacher has the answer as x=12, y=5 I

Algebra ->  Systems-of-equations -> SOLUTION: Solving systems of equations, use either substitution or elimination method. The problem I have is: 1/2x - 7/5y = -1 1/3 x + y = 9 My teacher has the answer as x=12, y=5 I      Log On


   

Question 490761: Solving systems of equations, use either substitution or elimination method.
The problem I have is:
1/2x - 7/5y = -1
1/3 x + y = 9
My teacher has the answer as x=12, y=5
I cannnot get this answer.
Thank you very much for your help!!! Cindy
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The problem I have is:
1%2F2x - 7%2F5y = -1
1%2F3x + y = 9
Get rid of these annoying fractions, multiply the 1st eq by 10, the 2nd eq by 3, result:
5x - 14y = -10
x + 3y = 27
we can use the 2nd equation for substitution
x = (-3y+27)
Substitute this for x in the 1st equation
5(-3y+27) - 14y = -10
-15y + 135 - 14y = -10
-15y - 14y = -10 - 135
-29y = -145
29y = 145; multiplied both sides by -1
y = 145%2F29
y = 5
:
Find x
we know x = -3y + 27, replace y with 5
x = -3(5) + 27
x = -15 + 27
x = 12, which is what the teacher said, but we can check it in the original eq
:
1%2F3x + y = 9
Replace x and y
1%2F3(12) + 5 = 9
4 + 5 = 9; confirms our solutions