6x - 3y + 2z = - 30

6x + 5y=-4

-6z = - 18

x = 251/765, y = 698/85, z = 7/3

Our solution set is (x, y, z) = (-4,4,3)

Step-by-step explanation:

Basically you take a look at the first equation it has the variable z, to find z we would have to solve for the 3rd equation which is:

-6z=-18

we divide both sides by - 6 to isolate z (that is - 6z/-6 which cancel out 6 and we are left with z and on the other side of equal sign we divide the - 18 by - 6 and we get 3 as our answer.

Now that we know z=3 We plug it's value for equation 2 i. e. 6x-3y+2z=-30

which becomes 6x+5y + (2*3) = -30

6x+5y+6=36 (now we have to combine 6 with the other number - 30. so we are left with variable one side and number on the other. to do this we subtract 6 from - 36 and you get:

6x+5y=-36

Now we solve for equation 2 to get the value of y:

6x+5y=-4

you move 6x to other side it becomes negative

5y=-4-6x

now you need to isolate y to do this you divide 5 from the equations on the right side.

so it will look like:

y = - 4/5-6x/5

also can write it as y=-6x/5-4/5

Now we now the value of y so now we can plug it in the 1st equation i. e.

6x - 3• (-6x/5-4/5) = - 36 (you use distributive property here to distribute it)

48x/5 = - 192/5

48x = - 192 (divide 48 from - 192 and you get - 4)

x = - 4

Now we now that

x = - 4

y=-6x/5-4/5

z=3

Now we are going to use x value to solve for y

y = (-6/5) (-4) - 4/5

and we get y=4

Our solution set is (x, y, z) = (-4,4,3)