I need help in algebra 2?ASAP?

Question

solve the system using any algebraic method.
x+3y+z=6
2x+2y-z=12
-x+6y+z=18

solve step by step ty

Answer 1

eq 1) x = 6-3y-z

eq 2) 2(6-3y-z)+2y-z=12
12-6y-2z+2y-z=12
-4y-3z=0
-4y=3z
y=-3/4*z
eq 3) -x=18-6y-z
x=-18+6y+z
eq1&eq3) compare x's => -18+6y+z=6-3y-z
-18+6(-3/4*z)+z=6-3(-3/4*z)-z
-18-18/4z+z=6+9/4z-z
-18-14/4z=6+5/4z
-24=19/4z

z=-96/19

Answer 2

the trick is to subtract each equation from each other in order to eliminate at least one variable.

x + 3y +z = 6
-x+ 6y +z = 18
--------------------
2x -3y = 12

notice how how i subtract a negative value. x- (-x) is equal to 2x

we then get the value of x as another equation
x = 3/2y - 6

we subtract two other equation to get another value of x

2x + 2y - z = 12
-x + 6y + z = 18 (-1)

notice that i multiplied the bottom equation to negative 1 so that i could again eliminate the variable z
we now have:

2x + 2y -z = 12
x - 6y - z = -18
----------------------
x -8y = 30

therefore x = 8y -30

we then equate both value of x, we will have

8y - 30 = 3/2y - 6

we can now have the value y

8v -3/2y = 30 - 6
(16y - 3y)/2 = 24
16y - 3y = 48
13y = 48
y = 3.692

using:
x = 8y - 30
x = 8(3.692) - 30
x = -0.464

then:

x + 3y +z = 6
-0.464 + 3(3.692) + z = 6
z = -4.612

notice that i use three decimal points in order to lessen decimal errors.

what do you think?

Answer 3

If you have a graphing calc, put the coefficients into Matrix A
1 3 1
2 2 -1
-1 6 1
And Solutions in Matrix B
6
12
8
Then do A^-1B

Answer 4

(1).....x +3y+z=6
(2).....2x+2y-z=12
(3)......-x+6y+z=18

(2) +(1)
3x +5y = 18 ..............(4)

(3) -(1)
-2x + 3y = 12 ...........(5)

(9) x 2 , (5) x 3;
6x + 10y = 36...........(6)
-6x + 9y = 36............(7)

(7) + (6)
y = 3.789 ..........ans.

subs . value of y into equation (4)
x = - 0.315........ans.


subs value of x and y into equation (1)
(-0.315) + 3(3.789) + z = 6
so , z = -5.052....ans

..... try check...........substitute all ans into equation (2) or (3).....
good luck..