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Solving 3 equations, 3 variables by the ELIMINATION METHOD?

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by Orla M » Fri Jan 11, 2013 2:53 am
Hi, I'm trying out different methods to solve this. Substition is fine, but getting stuck with the elimination method on this one to solve for w, x and y:

w-2x+3y=13
2w+x-4y=-14
3w-x-2y=8

Can you please help in explaining how we do this for 3 equations?

Thanks
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Source: — Problem Solving |

by Sam_hellboy » Fri Jan 11, 2013 3:23 am
w-2x+3y=13 - (1)
2w+x-4y=-14 - (2)
3w-x-2y=8 - (3)

Add Eqn 1 & 2. Result will be 3W - X - y = -1 - (4)

Now subtract Eqn (4) from eqn (3)

Result = -y = 9 => y = -9

Put y in Eqn(2)

2w+x+36=-14 ---(5)

Put y in Eqn (3)
3w-x+18=8 ----(6)

Add Eqn (5) & (6)

5W+54= -6 => W = -12

Now you have got the value for w & y. Put those in any equation and you will get x = -26.
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by GMATGuruNY » Fri Jan 11, 2013 3:32 am
Orla M wrote:Hi, I'm trying out different methods to solve this. Substition is fine, but getting stuck with the elimination method on this one to solve for w, x and y:

w-2x+3y=13
2w+x-4y=-14
3w-x-2y=8

Can you please help in explaining how we do this for 3 equations?

Thanks
Subtract the first two equations from the third to eliminate every variable but y:
(3w-x-2y) - (w-2x+3y) - (2w+x-4y) = 8 - 13 - (-14)

-y = 9

y = -9.

To solve for w, plug y = -9 into the second and third equations and add the two equations:
(2w + x - 4(-9)) + (3w - x - 2(-9)) = -14 + 8

5w + 54 = -6

w = -12.

To solve for x, plug w = -12 and y = -9 into the first equation:
-12 - 2x + 3(-9) = 13

-2x - 39 = 13

x = -26.
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