Solve the system of equations:   2x - 5y + 3z = -1 x + 4y - 2z = 9 x - 2y - 4z = -5

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We have to solve the following equations by elimination

2x-5y+3z=-1 ...(1)

x+4y-2z=9 ...(2)

x-2y-4z=-5 ...(3)

Let's eliminate x and create 2 equations with y and z.

(2) - (3)

=> 4y - 2z + 2y + 4z = 9+5

=> 6y + 2z = 14

=> 3y + z =...

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We have to solve the following equations by elimination

2x-5y+3z=-1 ...(1)

x+4y-2z=9 ...(2)

x-2y-4z=-5 ...(3)

Let's eliminate x and create 2 equations with y and z.

(2) - (3)

=> 4y - 2z + 2y + 4z = 9+5

=> 6y + 2z = 14

=> 3y + z = 7 ...(4)

(1) - 2*(2)

=> 2x - 5y + 3z - 2x - 8y + 4z = -1 - 18

=> -13y + 7z = -19 ...(5)

Now 7*(4) - (5)

=> 21y + 7z + 13y - 7z = 49 + 19

=> 34y = 68

=> y = 2

substitute in (4)

3y + z = 7

=> 6 + z = 7

=> z = 1

substitute y and z in (2)

=> x + 8 - 2 = 9

=> x = 3

Therefore x = 3, y= 2 and z = 1.

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