Question

perform an operation the given system that eliminates the x-term from the second question write the new equivalent system

x-2y-z=4 , x-y+3z=0, 4x+y+z=0

Answer 1

x - 2y - z = 4

x - y + 3z = 0

4x + y + z = 0

from equation 1

adding 2y and z on both sides

x = 2y + z + 4

plugging this value of x into equation 2

( 2y + z + 4) - y + 3z = 0

y + 4z + 4 = 0

subtrcating 4 from both sides

y + 4z = - 4 -----------------------(3)

so , we have eliminated x from 2nd equation

similarly eliminating x from 3rd equation

4 ( 2y + z + 4 ) + y + z = 0

8y + 4z - 16 + y + z = 0

9y + 5z =-16 ----------------------(4)

multiplying equation 3 by -9 and adding equation 5 to it

-9y - 36z = 36

9y + 5z = -16

------------------

- 31z = 20

z = -20/31

y = -4z - 4

y = -4 (-20/31 ) - 4

y = -44/31

plugging z and y into equation 1

x - 2( -44/31) - (-20/31 ) = 4

x = 16/31

solution is

x = 16/31 , y = - 44/31 , z = - 20/31