Algebra
posted by Mary on .
I need help I don't know how to solve this system
Solve the following system. Show all your work
3x2y+2z= 30
x+3y4z= 33
2x4y+3z= 42

Eq1: 3x2y+2z = 30
Eq2: x+3y4z = 33
Eq3: 2x4y+3z = 42
Multiply Eq1 by 2 and add Eq1 and Eq2:
6x4y+4z = 60
x+3y4z = 33
Eq4:5xy = 27 = Sum.
Multiply Eq2 by 3 and Eq3 by 4 and add Eq2 and Eq3:
3x+9y12z = 99
8x16y+12z = 168
Eq5: 5x7y = 69
Multiply Eq4 by 1 and add Eq4 and Eq5:
5x+y = 27
+5x7y = 69
Sum: 6y = 42
Y = 7
In Eq5, replace y with 7:
5x7*7 = 69
5x+49 = 69
5x=20
X = 4
In Eq1, replace x with 4, y with 7 and
solve for z:
3*42*7+2z = 30
12+14+2z = 30
2z = 3026 = 4
Z = 2.
SOLUTION SET: X = 4, Y = 7, Z = 2.
Y =
=