`2x + 3y =0, 4x + 3y - z = 0, 8x + 3y + 3z = 0` Solve the system of linear equations and check any solutions algebraically.

Eq1: `2x+3y=0`

Eq2:`4x+3y-z=0`

Eq3:`8x+3y+3z=0`

Multiply equation 2 by 3,

`12x+9y-3z=0` 

Now add the above equation and equation 3,

`(8x+3y+3z)+(12x+9y-3z)=0`

`8x+12x+3y+9y+3z-3z=0`

`20x+12y=0`

`4(5x+3y)=0`

`5x+3y=0`

Now let's solve the above equation and equation 1,

`2x+3y=0`

`5x+3y=0`

Subtract the above equations

`2x-5x=0`

`-3x=0`

`x=0`

Substitute back the value of x,

`2x+3y=0`

`2(0)+3y=0`

`3y=0`

`y=0`

Plug in the value of x and y in equation 2,

`4(0)+3(0)-z=0` ` `

`-z=0`

`z=0`

Solutions of the equations are x=0, y=0 and z=0

Eq1: `2x+3y=0`

Eq2:`4x+3y-z=0`

Eq3:`8x+3y+3z=0`

Multiply equation 2 by 3,

`12x+9y-3z=0` 

Now add the above equation and equation 3,

`(8x+3y+3z)+(12x+9y-3z)=0`

`8x+12x+3y+9y+3z-3z=0`

`20x+12y=0`

`4(5x+3y)=0`

`5x+3y=0`

Now let's solve the above equation and equation 1,

`2x+3y=0`

`5x+3y=0`

Subtract the above equations

`2x-5x=0`

`-3x=0`

`x=0`

Substitute back the value of x,

`2x+3y=0`

`2(0)+3y=0`

`3y=0`

`y=0`

Plug in the value of x and y in equation 2,

`4(0)+3(0)-z=0` ` `

`-z=0`

`z=0`

Solutions of the equations are x=0, y=0 and z=0