what is x,y,z for x+3y-z=11, -4x-3y-3z=-6, 3x+6y+5z=-8
Need Help with getting x,y,z
1) x + 3y - z = 11
2) -4x - 3y - 3z = -6
3) 3x + 6y + 5z = -8
Multiply equation 1 by 3.
3(x + 3y - z) = 11 * 3
4) 3x + 9y - 3z = 33
Subtract equation 2 from equation 4.
3x + 9y - 3z = 33)
-(-4x - 3y - 3z = -6)
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7x + 12y = 39
5) 7x + 12y = 39
Multiply equation 2 by 5.
5(-4x - 3y - 3z) = -6 * 5
6) -20x - 15y - 15z = -30
Multiply equation 3 by 3.
3(3x + 6y + 5z) = -8 * 3
7) 9x + 18y + 15z = -24
Add equation 7 to equation 6.
-20x - 15y - 15z = -30
+( 9x + 18y + 15z = -24)
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-11x + 3y = -54
8) -11x + 3y = -54
Multiply equation 8 by 4.
4(-11x + 3y) = -54 * 4
9) -44x + 12y = -216
Subtract equation 9 from equation 5.
7x + 12y = 39
-(-44x + 12y = -216)
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51x = 255
51x = 255
x = 255/51
x = 5 <<<<<<<<<<<<<<<<<<<<
Use equation 5 to solve for y.
7x + 12y = 39
7(5) + 12y = 39
35 + 12y = 39
12y = 39 - 35
12y = 4
y = 4/12
y = 1/3 <<<<<<<<<<<<<<<<<<<<
Use equation 3 to solve for z.
3x + 6y + 5z = -8
3(5) + 6(1/3) + 5z = -8
15 + 2 + 5z = -8
17 + 5z = -8
5z = -8 - 17
5z = -25
z = -25/5
z = -5 <<<<<<<<<<<<<<<<<<<<
Always use the original equations to check the answers.
1) x + 3y - z = 11
5 + 3(1/3) - (-5) = 11
5 + 1 + 5 = 11
11 = 11
2) -4x - 3y - 3z = -6
-4(5) - 3(1/3) - 3(-5) = -6
-20 - 1 + 15 = -6
-6 = -6
3) 3x + 6y + 5z = -8
3(5) + 6(1/3) + 5(-5) = -8
15 + 2 - 25 = -8
-8 = -8
The correct answer is: x = 5, y = 1/3, z = -5