SOLUTION: What is the solution to this system of linear equations using the substitution method? 1/2x-1/5y=6 1/6+2/5y=9

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Question 665403: What is the solution to this system of linear equations using the substitution method?
1/2x-1/5y=6
1/6+2/5y=9
Found 2 solutions by mananth, MathTherapy:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
%281%2F2%29x-%281%2F5%29y=6
%281%2F6%29xx%2B%282%2F5%29y=9


%281%2F2%29x-%281%2F5%29y=6
LCD = 10
multiply equation by 10
we get %2810%2F2%29x-%2810%2F5%29y=6%2A10
5x-2y=60...............(1)
%281%2F6%29x%2B%282%2F5%29y=9
Multiply equation by LCD 30
%2830%2F6%29x%2B%2830%2F5%29y=9%2A30
5x+6y=270................(2)
5 x -2 y = 60 .............1

5 x + 6 y = 270 .............2
Eliminate y
multiply (1)by 3
Multiply (2) by 1
15 x \ -6 y = 180
5 x + 6 y = 270
Add the two equations
20 x = 450
/ 20
x = 23
plug value of x in (1)
5 x -2 y = 60
113 -2 y = 60
-2 y = 60 -113
-2 y = -53
y = 26
x= 23
y= 26

m.ananth@hotmail.ca







Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

What is the solution to this system of linear equations using the substitution method?
1/2x-1/5y=6
1/6+2/5y=9



5x - 2y = 60 ----- Multiplying eq (i) by LCD, 10 ----- eq (iii)
5x + 12y = 270 ---- Multiplying eq (ii) by LCD, 30 ----- eq (iv)
- 14y = - 210 ------ Subtracting eq (iv) from eq (iii)

y = %28-+210%29%2F-+14, or highlight_green%28y+=+15%29

5x - 2(15) = 60 ------ Substituting 15 for y in eq (iii)
5x - 30 = 60
5x = 90
x = 90%2F5, or highlight_green%28x+=+18%29

You should be able to do the check, in the original equations, i.e. eqs (i) & (ii)

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