Posted by **Mary** on Monday, October 7, 2013 at 9:53am.

I need help I don't know how to solve this system

Solve the following system. Show all your work

3x-2y+2z= 30

-x+3y-4z= -33

2x-4y+3z= 42

- Algebra -
**Henry **, Tuesday, October 8, 2013 at 11:05pm
Eq1: 3x-2y+2z = 30

Eq2: -x+3y-4z = -33

Eq3: 2x-4y+3z = 42

Multiply Eq1 by 2 and add Eq1 and Eq2:

6x-4y+4z = 60

-x+3y-4z = -33

Eq4:5x-y = 27 = Sum.

Multiply Eq2 by 3 and Eq3 by 4 and add Eq2 and Eq3:

-3x+9y-12z = -99

8x-16y+12z = 168

Eq5: 5x-7y = 69

Multiply Eq4 by -1 and add Eq4 and Eq5:

-5x+y = -27

+5x-7y = 69

Sum: -6y = 42

Y = -7

In Eq5, replace y with -7:

5x-7*-7 = 69

5x+49 = 69

5x=20

X = 4

In Eq1, replace x with 4, y with -7 and

solve for z:

3*4-2*-7+2z = 30

12+14+2z = 30

2z = 30-26 = 4

Z = 2.

SOLUTION SET: X = 4, Y = -7, Z = 2.

Y =

=

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