Question

Solve the system, enter as an ordered triple. Need HELP!!

Answer 1

Answer:   (2,   3,   1)

This means x = 2, y = 3 and z = 1

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Work Shown:

Double everything in the second equation to get 4x-2y+4z=6

Add this result to the first equation

$x+2y-4z = 4\\4x-2y+4z = 6\\5x+0y+0z = 10$

The first two lines of that expression above shows us adding x+2y-4z=4 to the equation 4x-2y+4z = 6

The x terms add to x+4x = 5x

The y terms add to 2y+(-2y) = 0y

The z terms add to -4z+4z = 0z

The terms on the right hand side add to 4+6 = 10

That's how we end up with the new equation 5x+0y+0z = 10

That becomes 5x = 10 which solves to x = 2 when we divide both sides by 5.

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Use this x value in the third original equation to find z

3x-8z = -2

3(2)-8z = -2

6-8z = -2

-8z = -2-6

-8z = -8

z = -8/(-8)

z = 1

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Use the x and z values we found to find y

x+2y-4z = 4

2+2y-4(1) = 4

2+2y-4 = 4

2y-2 = 4

2y = 4+2

2y = 6

y = 6/2

y = 3

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Overall we get the solutions to be x = 2, y = 3 and z = 1

We can say the solution as an ordered triple is (x,y,z) = (2,3,1)