Find the ordered triplet $(x,y,z)$ for the following system of equations:
x + 3y + 2z= 1,
-3x + y + 5z = 10,-
2x - 3y +z =7.
What is x,y, and z?
+128475 x + 3y + 2z= 1 (1)
-3x + y + 5z = 10 (2)
-2x - 3y +z =7 (3)
Multiply the second equation by - 3
9x - 3y - 15z = -30 using equation 1
x +3y + 2z = 1 add these
10x - 13z = -29 (4)
Mutiply the second equation by 3
-9x + 3y + 15z = 30 using equation 3
-2x - 3y + z = 7 add these
-11x + 16z = 37 (5)
Multiply (4) through by 11 and (5) through by 10
110x - 143z = -319
-110x + 160z = 370 add these
17z = 51 divide through by 17
z = 3
Using (4)
10x - 13 (3) = -29
10x -39 = -29 add 39 to both sides
10x = 10
x = 1
Using (1)
x + 3y + 2z= 1
1 + 3y + 2(3) = 1
3y + 6 = 0
3y = - 6
y = -2
