SOLUTION: first clear of the fractions and then solve by substitution x/2 - y/3 = 5/6 x/5

SOLUTION: first clear of the fractions and then solve by substitution x/2 - y/3 = 5/6 x/5 - y/4 = 57/10

Question 712600: first clear of the fractions and then solve by substitution
x/2 - y/3 = 5/6
x/5 - y/4 = 57/10
Found 2 solutions by Menjax, DrBeeee:
Answer by Menjax(62) (Show Source): You can put this solution on YOUR website!
3x-2y/6 = 5/6
3x-2y=5 (equation 1)
4x-5y/20=114/20
4x-5y=114 (equation 2)
Sub 1 into 2
4(5+2y/3) -5y=114
20+8y/3 -5y/1 = 114
20-7y/3 = 114
-7y = 322
y=-46
sub y into 1
3s-2(46)=5
3x-92=5
3x=97
x=97/3
Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
Given
(1) x/2 - y/3 = 5/6 and
(2) x/5 - y/4 = 57/10
Clear the fractions in (1) by multiplying both sides of the equation by 6 and get
(3) 3x - 2y = 5
Clear the fractions in (2) by multiplying both sides of the equation by 20 and get
(4) 4x - 5y = 114
Now solve (3) for x and get
(5) 3x = 2y + 5 or
(6) x = (2/3)y + 5/3
Now substitute x of (6) into (4) and get
(7) 4*((2/3)y + 5/3) - 5y = 114 or
(8) (8/3)y + 20/3 - 5y = 114 or
(9) (8/3 - 5)y = 114 - 20/3 or
(10) ((8-15)/3)y = (342-20)/3 or
(11) -(7/3)y = 322/3 or
(12) -7y = 322 or
(13) y = -322/7 or
(13) y = -46
Use y of (13) in (6) to get x
(14) x = (2/3)(-46) + 5/3 or
(15) x = (-92 + 5)/3 or
(16) x = -87/3 or
(17) x = -29
Check this pair with (2).
Is (-29/5 -(-46)/4 = 57/10)?
Is ((-29*4 + 46*5)/20 = 57/10)?
Is ((-116 + 230)/20 = 57/10)?
Is (114/20 = 57/10)?
Is (57/10 = 57/10)? Yes
Answer: The solution pair, using fraction clearing and substitution, is
(-29,-46)
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