find ordered triple of thsese equations. 4x+6y+8z=-10, 4x+2y-6z=8, 2x+8y-6z=0
which ordere4d triple is a solution of the system of equations?
1) 4x + 6y + 8z = -10
2) 4x + 2y - 6z = 8
3) 2x + 8y - 6z = 0
Multiply equation 1 by 6.
6(4x + 6y + 8z) = -10 * 6
4) 24x + 36y + 48z = -60
Multiply equation 2 by 8.
8(4x + 2y - 6z) = 8 * 8
5) 32x + 16y - 48z = 64
Add equation 5 to equation 4.
24x + 36y + 48z = -60
+(32x + 16y - 48z = 64)
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56x + 52y = 4
6) 56x + 52y = 4
The z co-efficients of equations 2 and 3 are already the
same, so subtract equation 3 from equation 2.
4x + 2y - 6z = 8
-(2x + 8y - 6z = 0)
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2x - 6y = 8
7) 2x - 6y = 8
Multiply equation 6 by 6.
6(56x + 52y) = 4 * 6
8) 336x + 312y = 24
Multiply equation 7 by 52.
52(2x - 6y) = 8 * 52
9) 104x - 312y = 416
Add equation 9 to equation 8.
336x + 312y = 24
+(104x - 312y = 416)
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440x = 440
440x = 440
x = 1 <<<<<<<<<<<<<<<<<<
Use equation 7 to calculate the value of y.
2x - 6y = 8
2(1) - 6y = 8
2 - 6y = 8
-6y = 8 - 2
-6y = 6
y = 6 / -6
y = -1 <<<<<<<<<<<<<<<<<<
Use equation 3 to calculate the value of z.
2x + 8y - 6z = 0
2(1) + 8(-1) - 6z = 0
2 - 8 - 6z = 0
-6 - 6z = 0
-6z = 0 + 6
-6z = 6
z = 6 / -6
z = -1
Use all three of the problem's equations to check your answers.
1) 4x + 6y + 8z = -10
4(1) + 6(-1) + 8(-1) = -10
4 - 6 - 8 = -10
-10 = -10
2) 4x + 2y - 6z = 8
4(1) + 2(-1) - 6(-1) = 8
4 - 2 + 6 = 8
8 = 8
3) 2x + 8y - 6z = 0
2(1) + 8(-1) - 6(-1) = 0
2 - 8 + 6 = 0
0 = 0
The answer is: x = 1, y = -1, z = -1