SOLUTION: / = a fraction x/2 - y/3 = 5/6 x/5 - y/4 = 43/10 what is the solution to the system of equations by using substitution?

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Question 636588: / = a fraction
x/2 - y/3 = 5/6
x/5 - y/4 = 43/10
what is the solution to the system of equations by using substitution?
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
x%2F2+-+y%2F3+=+5%2F6.....1
x%2F5+-+y%2F4+=+43%2F10......2
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x%2F2+-+y%2F3+=+5%2F6.....1..solve for x
x%2F2=+y%2F3+%2B+5%2F6
x=+%282%2F3%29y+%2B10%2F6
x=+%282%2F3%29y+%2B5%2F3......plug it in 2
____________________________________
x%2F5+-+y%2F4+=+43%2F10......2

%282%2F3%29y+%2B5%2F3%29%2F5+-+y%2F4+=+43%2F10...solve for y

%28%282%2F3%29y+%2B5%2F3%29%2F5+-+y%2F4+=+43%2F10..both side multiply by 20

20%28%282%2F3%29y+%2B5%2F3%29%2F5+-+20y%2F4+=+20%2A43%2F10



4%28%282%2F3%29y+%2B5%2F3%29+-+5y+=+2%2A43

%288%2F3%29y+%2B20%2F3+-+5y+=+86..both side multiply by 3

%288%2F3%29%2A3y+%2B20%2A3%2F3+-+5%2A3y+=+86%2A3

%288%2Fcross%283%29%29%2Across%283%29y+%2B20%2Across%283%29%2Fcross%283%29+-+5%2A3y+=+86%2A3

8y+%2B20+-15y+=+258
-7y+=+258-20
-7y+=+238
y+=+238%2F-7

highlight%28y+=+-34%29
now find x
x=+%282%2F3%29y+%2B5%2F3%7D..plug+in+%7B%7B%7By
x=+%282%2F3%29%28-34%29+%2B5%2F3
x=+%280.67%29%28-34%29+%2B1.67
x=+-22.666666666666666666666666666667+%2B1.67
x=-20.999999999999999999999999999993
round to whole number
highlight%28x=-21%29



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

/ = a fraction
x/2 - y/3 = 5/6
x/5 - y/4 = 43/10
what is the solution to the system of equations by using substitution?

x%2F2+-+y%2F3+=+5%2F6

3x - 2y = 5 ------ Multiplying by LCD, 6 ----- eq (i)

x%2F5+-+y%2F4+=+43%2F10

4x - 5y = 86 ----- Multiplying by LCD, 20 ------ eq (ii)

3x - 2y = 5 ------ eq (i)
4x - 5y = 86 ----- eq (ii)
- 15x + 10y = - 25 ----- Multiplying eq (i) by - 5 ------ eq (iii)
8x - 10y = 172 ----- Multiplying eq (ii) by 2 ------ eq (iv)
- 7x = 147 ----- Adding eqs (iv) & (iii)
x = 147%2F-+7, or highlight_green%28-+21%29

- 63 - 2y = 5 ----- Substituting - 21 for x in eq (i)

- 2y = 5 + 63

- 2y = 68
y = 68%2F-+2, or highlight_green%28-+34%29

You should be able to do your own check!!

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