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Solve the system of equations. 3x+4y+4z=4, 5x+7y+3z=5 and 4x+5y+7z=7

User Ma Kobi
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2 Answers

3 votes

Answer:

Its C

Step-by-step

correct edge 2021

User Chetya
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We'll label the equations to keep track of what we're doing

3x+4y+4z=4 A

5x+7y+3z=5 B

4x+5y+7z=7 C

Normally in Gaussian elimination we'd pick put a constant on each equation and combine to cancel out a variable in all but one. But here we have an opportunity to make the coefficient 1 on our variables in at least one equation. This is a pretty good thing to do when solving these by hand.

x + y + 3z = 3 D=C-A

-2x - 3y + z = -1 E=A-B

Let's eliminate x from two equations

-y + 7z = 5 F=2D+E

-y + 5z = 5 G=4D-C

Let's eliminate y

2z = 0 H=F-G

z = 0

-y + 7z = 5

y = -5

x + y + 3z = 3

x - 5 + 0 = 3

x = 8

Answer: (x,y,z)=(8,-5,0)

Check:

3(8)+4(-5)+4(0) = 4, good

5(8)+7(-5)+3(0)=5, good

4(8)+5(-5)+7(0)=7, good

User Luisfarzati
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