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Mathematics
Ellie Blair
4 January, 15:07
6x - 3y + 2z = - 30
6x + 5y=-4
-6z = - 18
+5
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Maverick Vaughan
4 January, 15:37
0
x = 251/765, y = 698/85, z = 7/3
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Valeria Hess
4 January, 16:17
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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)
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