Solve the following system of equations for all three variables. -2x + 3y – 4z = 8
5x – 3y + 5z = -8
7x – 3y + 3z = 8
X =
1
y =
2
Z =
3
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Step-by-step explanation:

-2x + 3y – 4z = 8    (I)

5x – 3y + 5z = -8    (II)

7x – 3y + 3z = 8 (III)

Add equation (I) & (II) and thus y will be eliminated

(I)        -2x + 3y – 4z = 8

(II)        5x – 3y + 5z = -8    {Add}

           3x          + z  = 0   (A)

Multiply equation (II) by (-1) and then add with equation (III). Thus y will be eliminated.

(II) * (-1)         -5x + 3y - 5z = +8

                     7x – 3y + 3z = 8   {Add}

                     2x         -2z   = 16   (B)

Multiply equation (A) by 2 and then add. Thus z will be eliminated and we will get the value of x

(A) * 2          6x + 2z = 0

(B)                 2x - 2z  = 16   {Add}

                     8x         = 16

Divide both sides by 8

                             x = 16/8

                          x = 2

Plugin x = 2 in equation (A)

3x + z = 0

3*2 + z = 0

 6 + z = 0

       z = -6

Plug in x = 2 and z  = - 6 in equation (I)

-2x +3y - 4z = 8

-2*2 + 3y - 4*(-6) = 8

-4 + 3y + 24 = 8

     3y   + 20 = 8

               3y = 8 - 20

               3y = -12

                 y = -12/3

y = -4

Given equations

2x+3y−z=6  →(1)

x−y+7z=8    →(2)

3x−y+2z=7     →(3)

(1)+3×(2)  

2x+3y−z+3x−3y+21z=6+24

5x+20z=30

x+4z=6    →(4)

(3)−(2)

2x−5z=−1   →(5)

2×(4)−(5)

2x+8z−2x+5z=12=1

13z=13

z=1

x=6−4z  

x=2

⇒  2(2)+3y−1=6

y=1

∴   x=2,y=1,z=1 is solution of given equations.

Step-by-step explanation: hope it is help full

m a t h w a y. c o m

step-by-step explanation: