Use the 5-step procedure to solve by elimination: x - y - 2z = 4, -x + 2y + z = 1, and -x + y - 3z = 11. Write your answer as a point, an ordered triple: (x,y,z), without spaces.

Answer 1

add first and last equations to eliminate x and y

-5z= 15

z = 15/-5 = -3

add the first two equations to eliminate x,

y-z = 5

substitute z=-3 into the above to eliminate z

y-(-3)= 5

y= 5-3= 2

y= 2, z = -3

substitute those values into any of the 3 original equations to solve for x

x-y-2z = 4

x-2 -2(-3) = 4

x = 4-6+2 = 0

(x,y,z) = (0,2,-3)

plug those values into the other two equations to check for possible error

Answer 2

Hi Lysandra O.

(0,2,-3)

Look closely at your equations

Both x and y can be eliminated first and z can be solved for

x - y - 2z = 4

-x +2y +z = 1

-x + y - 3z = 11

Combining the first and last equations eliminates both x and y leaving only z we can solve for z

x - y - 2z = 4

-x + y - 3z = 11

-5z = 15

Divide both sides by negative 5

z = -3

Combining the first two equations eliminates x and we can substitute - 3 for z to find y

x - y - 2z = 4

-x +2y +z = 1

y -z = 5

Substituting -3 for z

y -(-3) =5

y + 3 = 5

Subtract 3 from both sides

y = 5 - 3

y = 2

Now we have both y and z we can calculate x. I will use the first equation

x -y - 2z = 4

x -2 -2(-3) = 4

x - 2 + 6 = 4

x + 4 = 4

Subtract 4 from both sides

x = 0

You can the values in all of the equations give it a try