Answer:
(-6,9,-3)
Step-by-step explanation:
-3x -y +z=6
-3x-y+3z =0
x-3z =3
Multiply the second equation by -1
-1 *(-3x-y+3z) =0*-1
3x +y -3z =0
Add this to the first equation
-3x -y +z=6
3x +y -3z =0
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0 + 0 + -2z = 6
Divide by -2
-2z/-2 = 6/-2
z = 6/-2
z=-3
Take the third equation to find x
x-3z=3
x-3(-3) = 3
x+9=3
Subtract 9 from each side
x+9-9 =3-9
x=-6
Now we need to find y
3x +y -3z =0
3(-6) +y -3(-3) =0
-18 +y +9=0
-9+y =0
Add 9 to each side
-9+9+y = 0+9
y=9
(-6,9,-3)
Set of equations that can be used to calculate rate for each plumber:
2A+8B+8C = 1,400 --- (1)
4A+7B+10C = 1,660 --- (2)
3A+9B+9C = 1,660 --- (3)
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2*(1) - (2)
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4A+16B+16C = 2,800
4A+7B+10C = 1,660 -
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9B+6C = 1,140 --- (4)
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3(2) -4(3)
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12A+21B+30C = 4,980
12A+36B+36C = 6,600 -
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-15B-6C = -1,620 --- (5)
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(4) + (5)
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9B+6C = 1140
-15B-6C = -1620 +
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-6B = -480 => 6B = 480 => B = 480/6 = 80
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Using (4), 9(80)+6C = 1140
720+6C = 1140 => 6C = 1140-720 = 420 => C = 420/6 = 70
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Using (1), 2A+8(80)+8(70) = 1400
2A+640+560 =1400 => 2A = 1400-640-560 = 200 => A = 200/2 = 100
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The rates are:
A = $100
B = $80
C = $70
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On Thursday, number of calls: A = 4 hrs, B = 6 hrs, C = 3 hrs
Money earned = 4*100+6*80+3*70 = $1,090
