# Algebra

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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 -

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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