Question

What is the solution of the system of equations?

-3x-4y-3z=-7
2x-6y+2z=3
5x-2y+5z=9

Answer 1

If you have a TI-83 plus or higher, you could create a matrix and use rref to get the solution.

Let's begin with eliminating the y's in equations 1 and 3, then in equations 2 and 3:

`-3x-4y-3z=-7` times -1⇒
`3x+4y+3z=7`

`5x-2y+5z=9` times 2⇒
`10x-4y+10z=18`

ADD the two equations: 13x + 13z = 25


`2x-6y+2z=3` times -1⇒
`-2x+6y-2z=-3`

`5x-2y+5z=9` times 3⇒
`15x-6y+15z=27`

ADD the two equations: 13x+13z=24

Subtract the two resulting equations and you get 0 = 1 which is false so there is no solution for the system.

Answer 2

Given equations have no solution

Explanation:

Given -

Three set of equations -

`-3x-4y-3z=-7\\2x-6y+2z=3\\5x-2y+5z=9`

We will now equate "x" in the first equation in terms of "y" and "Z" and put it in second equation -

`-3x-4y-3z=-7\\x = (1)/(3) (-4y -3z+7)\\(2)/(3)(-4y -3z+7) -6y+2z=3\\-8.667 y = -1.667\\y = 0.192\\`

We will substitute the value of y in the under given equation-

`x = (1)/(3) (-4y -3z+7)\\x = (1)/(3) (-4*0.192 -3z+7)\\x= 2.077-z`

substituting the derived values in last equation, we get -

`5x-2y+5z=9\\5(2.077-z)-2(0.192)+5z=9\\10.385-5z-0.384+5z=9\\0=-1`

Hence, the given equations have no solution