Answer:
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)
