Question

How do you solve the system of equations algebraically `1.8x-z=0.7, 1.2y+z=-0.7, 1.5x-3y=3`?

Answer 1

`x=0.5`, `y=-0.75` and `z=0.2`

Explanation:

The three equations are

`1.8x-z=0.7` ...........................(1)

`1.2y+z=-0.7` ...........................(2)

`1.5x-3y=3` ...........................(3)

Note that adding (1) and (2) eliminates `z` and we get

`1.8x+1.2y=0` ...........................(4)

Now multiplying (3) by `6` and (4) by `5`, we get

`9x-18y=18` and `9x+6y=0` and subtracting latter from former, we get `-18y-6y=18-0` i.e. `-24y=18`

Hence `y=-18/24=-0.75`.

Putting this in (3) we get

`1.5x-3xx(-0.75)=3` or `1.5x=3-2.25=0.75`

Hence `x=0.75/1.5=0.5`

Now putting this in (1) , we get

`1.8xx0.5-z=0.7` or `0.9-z=0.7` i.e.

`z=0.9-0.7=0.2`

Hence solution is `x=0.5`, `y=-0.75` and `z=0.2`