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3 years ago

Solve the following system equations:

2 answers:

azamat3 years ago

7 0

(1).. 2x + 4y - 3z = -7
(2).. 3x + 1y + 4z = -12 
(3).. 1x + 3y + 4z = 4 

****************** 
ok.. we're going to put this into matrix form.. where we drop x, y, and z 
2.. 4.. -3.. | ... -7 
3.. 1.. .4.. | ... -12 
1.. 3.. .4 . | ... 4 
ok? 

now.. I'll designate the rows (1), (2), (3).. ok? 
new (1) = -2x(3) + (1) 
new (2) = -3x(3) + (2) 
ie... 
0..-2..-11. | .. -15 
0..-8.. -8.. | ... -24 
1.. 3.. .4 . | ... .+4 

new row (2) = old (2) / -8 
0..-2..-11. | .. -15 
0.. 1.. 1.. | ... +3 
1.. 3.. .4 . | ... +4 

new (1) = 2xold(2) + 1 
new (3) = -3xold(2) + 3 
0.. 0..-9 .. | ... -9 
0.. 1.. 1.. | ... +3 
1.. 0.. .1 . | ... -5 

new row(1) = old row 1 /-9 
0.. 0.. .1 .. | ... +1 
0.. 1.. 1.. | ... +3 
1.. 0.. .1 . | ... -5 

new (2) = old(2) - old(1) 
new (3) = old(3) - old(1) 
0.. 0.. .1 .. | ... +1 
0.. 1.. 0.. | ... +2 
1.. 0.. .0 . | ... -6 

so.. (x,y,z) = (-6, +2, +1)..

the last answer is correct

adell [148]3 years ago

3 0

Answer:

The solution is (–6, 2, 1). (Option A)

Step-by-step explanation:

Given three equations

2x + 4y - 3z = -7 → (1)

3x + y + 4z = -12 → (2)

x + 3y + 4z = 4 → (3)

we have to find the solution of above equations.

By elimination method

Multiply equation (2) by 4 and then subtracting from (1), we get

(2x + 4y - 3z+7)-4(3x + y + 4z + 12)=0

⇒ -10x-19z=41 → (4)

Multiply equation (2) by 3 and then subtracting from (3), we get

(x + 3y + 4z - 4)-3(3x + y + 4z + 12)=0

⇒ -8x-8z=40 ⇒ x+z=-5 → (5)

Solving (4) and (5), we get

-10x-19z-41+10(x+z+5)=0

⇒ -9z=-9 ⇒ z=1

⇒ x+1=-5 ⇒ x=-6

and (3) implies -6 + 3y + 4 = 4 ⇒ y=2

Hence, the solution of above 3 equations will be (x,y,z)=(-6,2,1)

Hence, option (1) is correct.

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Answer:

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Step-by-step explanation:

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3 years ago

PLEASE HELP! Calculate $40^{13} \pmod{85}.$

SVEN [57.7K]

In this type of calculations, we decompose 13 by checking the lowest powers of the base, that is 40. for example we check 40^2, or 40^3 and compare it to 85

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40*40*40=64,000

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64,000/85=752.94

85*753=64,005; 64000-64,005=-5

this means that

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$40^{13} =40^{3*4+1}={(40^{3})}^{4}*40=(-5)^{4}*40 \pmod{85}=\\\\625*40\pmod{85}=(7*85+30)*40\pmod{85}=30*40\pmod{85}\\\\=1200\pmod{85}=(14*85+10)\pmod{85}=10\pmod{85}$

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3 years ago

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So it can be

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3 years ago

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11Alexandr11 [23.1K]

Answer:

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Step-by-step explanation:

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Then you would want to solve. So, you would need to divide 2 by 1/3 which would give you 9.

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3 years ago