Question

For my practice equations, it is asking to Solve the system by elimination resulting in (x, y, z) ordered pair. I'm unsure how to approach given the variable arrangement.

Answer 1

Given

6x -6z =6........Equation (i)

-3x -5y =5 ......Equation (ii)

2y- 6z =4 ........Equation (iii)

Using elimination method

To eliminate X , multiply equation (ii) by 2 and the add

$\begin{gathered} 6x-6z=6........Equation(i) \\ -3x-5y\text{ =5 }\ldots..Equation\text{ (i}i)\text{ }\times2\text{ =-6x-10y=10} \\ 6x-6x-6z-10y=6+10 \end{gathered}$$-6z-10y=16$

-6z -10y =16 .......Equation (iv)

Rearrange

-10y-6z=16 .......Equation (iv)

2y -6z =4 .......Equation (iii)

To eliminate Z in Equation (iv) and Equation (iii)

Then We subtract

-10y-2y -6z-(-6z) =16 -4

-12y =12

Divide both sides by -12

y= -1

We can substitute for y in equation (iii)

2(-1) -6z=4

-2-6z =4

collect the like terms

-6z= 4+2

-6z=6

Divide both sides by 6

z= -1

Using equation (i)

substitute for z to get x

6x -6(-1) =6

6x +6=6

Collect the like terms

6x = 6-6

6x=0

Divide both sides by 6

x=0

The final answer

X= 0

Y= -1

Z =