Solve the system using elimination

Question

Solve the system using elimination

 

6x+5y+5z=6

-5x+2y-6z=-8

-5x+5y+2z=35

 

x=?

y=?

z=?

Answer 1

I'm going to number the equations to, hopefully, make it easier to follow.

6x + 5y + 5z = 6 (#1)       -5x + 2y - 6z = -8 (#2)    -5x + 5y + 2x = 35 (#3)

 

Multiply -1(#3) and add to (#1)

6x + 5y + 5z = 6

5x - 5y - 2z = -35 (#4)

11x + 3z = -29 (#5)

 

Multiply 5(#2) and -2(#3) and add together.

-25x + 10y - 30z = -40 (#6)

10x - 10y - 4z = -70  (#7)

-15x - 34z = -110  (#8)

 

Multiply 15(#5) and 11(#8) and add them together.

165x + 45z = -435 (#9)

-165x -374z = -1210  (#10)

         -329z = -1645

                z = 5 Substitute this value into (#5)

11x + 3(5) = -29

11x + 15 = -29

11x = -44

x = -4    Now, substitute the values for x and z into (#1).

6(-4) + 5y + 5(5) = 6

-24 + 5y + 25 = 6

5y +1 = 6

5y = 5

y = 1  (-4, 1, 5) 

 

Wasn't that fun?!!

 

 

 

 

 

 

Multiply 5(#2) and -2(#3) and add them together.