SOLUTION: 2/5x+3/4y=5/2 -2/3x+1/2y=3/4 find answer in substitution and show all your work

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Question 1035180: 2/5x+3/4y=5/2
-2/3x+1/2y=3/4 find answer in substitution and show all your work
Found 2 solutions by josmiceli, stanbon:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1) +%282%2F5%29%2Ax+%2B+%283%2F4%29%2Ay+=+5%2F2+
(2) +%28-2%2F3%29%2Ax+%2B+%281%2F2%29%2Ay+=+3%2F4+
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Multiply both sides of (1) by +20+
Multiply both sides of (2) by +12+
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(1) +8x+%2B+15y+=+50+
(2) +-8x+%2B+6y+=+9+
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Add the equations
+21y+=+59+
+y+=+59%2F21+
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and
(2) +-8x+%2B+6%2A%28+59%2F21+%29+=+9+
(2) +8x+=+118%2F7+-+63%2F7+
(2) +8x+=+55%2F7+
(2) +x+=+55%2F56+
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check the answers:
(1) +%282%2F5%29%2Ax+%2B+%283%2F4%29%2Ay+=+5%2F2+
(1) +%282%2F5%29%2A%2855%2F56%29+%2B+%283%2F4%29%2A%2859%2F21%29+=+5%2F2+
(1) +22%2F56+%2B+59%2F28+=+5%2F2+
(1) +22%2F56+%2B+118%2F56+=+140%2F56+
(1) +140%2F56+=+140%2F56+
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You can check (2)

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!

find answer in substitution
2/5x+3/4y=5/2
-2/3x+1/2y=3/4
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Solve the 1st eq for "y"::
y = [(-2/5)/(3/4)]x + (5/2)/(2/5)
------
y = (-3/10)x + (25/4)
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Substitute for "y" and solve for "x"::
(-2/3)x + (1/2)[(-3/10)x + (25/4)] = (3/4)
-------
(-2/3)x + [(-3/20)x + (25/8)] = 3/4
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[(-2/3)-(3/20)]x = (6/8)-(25/8)
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[(-40 - 9)/60]x = (48-200)/64
(-49/60)x = (-152/64)
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x = (-60/49)(-152/64)
x = 2.908
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Solve for "y"::
y = (-3/10)x + (25/4)
y = -0.3*2.908 + 25/4
y = 5.38
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Cheers,
Stan H.
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