Expert: Sherman D. - 7/2/2005

Question
What is the solution to the system containing these equations?
-6x+3y=33
-4x+y=16

Answer
Depending on how you want this done, i will do it 3 different ways

Elimination
-6x + 3y = 33
-4x + y = 16

Multiply bottom by -3

-6x + 3y = 33
12x - 3y = -48

the 3y's cancel out

-6x = 33
12x = -48

becomes

6x = -15

x = (-5/2)

-6x + 3y = 33
-6(-5/2) + 3y = 33
(30/2) + 3y = 33
15 + 3y = 33
3y = 18
y = 6

ANS : x = (-5/2), y = 6

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Addition
-6x + 3y = 33
-4x + y = 16

(-6x + 3y) + (-4x + y) = 33 + 16
-6x + 3y - 4x + y = 49
-10x + 4y = 49
4y = 10x + 49
y = (5/2)x + (49/4)

-4x + ((5/2)x + (49/4)) = 16
-4x + (5/2)x + (49/4) = 16
(-3/2)x + (49/4) = 16
(-3/2)x = (15/4)
-3x = (15/2)
x = (-5/2)

y = (5/2)(-5/2) + (49/4)
y = (-25/4) + (49/4)
y = (24/4)
y = 6

ANS : x = (-5/2), y = 6

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Subtraction
-6x + 3y = 33
-4x + y = 16

(-6x + 3y) - (-4x + y) = 33 - 16
-6x + 3y + 4x - y = 17
-2x + 2y = 17
-x + y = (17/2)
y = x + (17/2)

-4x + (x + (17/2)) = 16
-4x + x + (17/2) = 16
-3x = (15/2)
x = (-5/2)

y = (-5/2) + (17/2)
y = (12/2)
y = 6

I mostly did that so you know how to do any problems that asks for it.