Solve the system for each variable, and check your solutions.

Question

12. x + y + z = 6 and 2x – y + z = 3 and x + 2y – 3z = -4

13. x + y + z = 12 and x + 2y + 3z = 31 and 9y + z = 1

Answer 1

13 subtract the 1st and 2nd equations to get y+2z = 19.

then multiply the 3rd equation by 2 to get 18y+2z=2

subtract y+2z= 19 from 18y+2z=2 gives 17y =-17, y= -1

2z = 19+1+20, z=10

plug z=10 and y=-1 into either the 1st or 2nd equation to solve for x = 12-10+1 = 3

x=3, y=-1, z=10

13 add 1st 2 equations to get 3x+2z= 9

add twice the 2nd to the 3rd to get 5x -z = 4

multiply by to get 10x-2z = 4

add 3x+2z =9 to

get 13x= 11

x=13/13 =1

z=3

y=2

x=1,y=2, z= 3

solution is 1,2,3 for x,y,z

as simple as 1,2,3, A,B,C or X,Y,Z