Question 165401: Below are the equations that I need assistance with...
1. 2x+y-3z=-4
2. 4x-2y+z=9
3. 3x+5y-3z=5
Below are the instructions to solving the problems. I am supposed to solve for x, y, and z. The answer should be the same for x, y, and z in all three equations. For instance, if x is 2, y is 5, and z is 3 in problem #1, the answer should be the same for the last two problems. My professor explained this to me, but when I tried to solve it, I did not receive the correct answer. Please help me. I would really appreciate it. I need this answer for my class as soon as possible...
1.Choose two of the three equations so that one of the variables is eliminated (use addition method).
2.Repeat step one with two different equations to eliminate the same variable.
3.Use the equation resulting from steps 1 & 2 to solve for one of the variables.
4.Substitute the variable in step 3 into equation to solve for a second variable.
5.Substitute the values from steps 3&4 into equations 1, 2, or 3 to solve for the final variable.
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! 1. 2x+y-3z=-4
2. 4x-2y+z=9
3. 3x+5y-3z=5
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Multiply eqn 2 by 3
12x-6y+3z=27
Add to eqn 1 and to eqn 3
1. 2x+y-3z=-4
12x-6y+3z=27
14x-5y = 23 No z term
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3. 3x+5y-3z=5
12x-6y+3z=27
15x-y = 32 No z here either
Now there are 2 eqns in 2 unknowns:
14x-5y = 23
15x- y = 32 Multiply this by 5 to get the same y coefficient
75x-5y = 160
14x-5y = 23 Subtract this from it
61x = 137
x = 137/61 Answer for x
Sub x into 15x -y = 32
15*(137/61) - y = 32
y = (15*137 - 32*61)/61
y = 103/61 Answer for y
Sub x and y into any of the 3 original eqns, I'll use #1
1. 2x+y-3z=-4
2*(137/61) + (103/61) - 3z = -244/61
-3z = (-244 - 274 - 103)/61
-3z = -621/61
z = 207/61
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