# Use the elimination method to solve the system. x          +         y          +         z          =         2 5x        +        ...

Use the elimination method to solve the system.

x          +         y          +         z          =         2

5x        +         4y        +         3z        =         2

−3x     +         y          −         z          =         2

llltkl | Student

`x+y+z=2` ..........(i)

`5x+4y+3z=2` ............(ii)

`−3x+y−z=2` ...................(iii)

To eliminate z, from (i), (iii) perform (i)+(iii):

`x+y+z=2`

`−3x+y−z=2`

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

`-2x+2y=4`

`rArr -x+y=2` .................(iv)

Again, To eliminate z, from (i), (ii) perform (i)*3-(ii):

`3x+3y+3z=6`

`5x+4y+3z=2`

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

`-2x-y=4` ...........................(v)

Now to eliminate y from (iv), (v), perform (iv)+(v):

`-x+y=2`

`-2x-y=4`

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

`-3x=6`

`rArr x=-2`

Substituting x=-2 in equation (iv), get:

`-(-2)+y=0`

`rArr y=0`

Finally, put the values of x and y in equation (i) to get:

`-2+0+z=2`

`rArr z=2+2=4`

Therefore, the solutions are `x=-2, y=0, z=4`

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

Check:

(i) -2+0+4=2

(ii) 5*-2+4*0+3*4=-10+12=2

(iii) -3*-2+y*0-4=6-4=2