SOLUTION: solve the system: x+3y+5z=20 y-4z=-16 3x-2y+9z=36

Question 152808: solve the system:
x+3y+5z=20
y-4z=-16
3x-2y+9z=36
Answer by Electrified_Levi(103) (Show Source): You can put this solution on YOUR website!
Hi, Hope I can help,
.
solve the system:
.
x+3y+5z=20
y-4z=(-16)
3x-2y+9z=36
.
This is the way I usually solve these problems(pretty easy once you know how to do it) ( There is no fast way to solve these problems)
.
First, solve for a letter in all the equations( since we already have a 2 system/variable equation for equation 2, we don't have to solve for any letter in equation 2)( Since that means we will need to solve for "x" in our other equations)
.
We will rewrite the 3 equations so it makes more sense( the second equation has no "x's" in the equation so it has "0x")
.

x+3y+5z=20
0x + y - 4z =( -16)
3x-2y+9z=36
.
We will switch the equations around
.
x+3y+5z=20
3x-2y+9z=36
0x + y - 4z = (-16)
.
We will solve "x" in our first two equations(can't solve "x" in our third equation, since it is 0x)
.
First equation
.

.
We will move "3y" over to the right side
.
=
.
=
.
We will move "5z" to the right side
.
=
.
=
.
We will switch the letters around
.
=
.
This is our First Answer
.
We will now solve "x" in our second equation
.

.
We will move (-2y) to the right side
.
=
.
=
.
We will move "9z" to the right side
.
=
.
=
.
We will switch the letters around
.
=
.
We will now divide each side by "3"
.
=
.
=
.

.
Our second answer =
.
We can now solve to get a 2 system(variable) equation
.
We will put our two answers together in an equation, since "x" = both of the answers, our answers equal each other
.
First answer =
.
Second answer =
.
Our equation will equal
.
=
.
We will use cross multiplication to get rid of the fractions
.

.
We will move (-9y) to the right side
.

.
=
.
We will move the (-15z) to the right side
.
=
.
=
.
We will move the "36" to the left side
.
=
.
=
.
We will rearrange, =
.
Our second 2 system/variable equation =
.
We will put our two 2 system/variable equations side by side
.
First equation =
.
Second equation =
.

.
We will now need to solve for a letter again( we will solve "y" since it is the easiest to solve)
.
First equation
.
We will move (-4z) to the right side
.
=
.
=
.
= ( rearranging the numbers)
.
Our first answer =
.
Our second equation
.
We will move "6z" to the right side
.
=
.
=
.
Rearranging =
.
We will divide each side by "11"
.
=
.
=
.
=
.
Our second answer is
.
We can now put both of our answers into an equation( since "y" equals both of our answers)
.
Answer 1 =
.
Answer 2 =
.
We can make our equation, it equals
.
=
.
We will cross multiply to get rid of the fractions
.

.
It becomes,
.
We will move (-6z) to the left side
.
=
.
=
.
We will move (-176) to the right side
.
=
.
=
.
We will divide each side by "50"
.
=
.
=
.
=
.
We found that "z" = 4, we can replace "z" with "4" in one of our 2 system/variable equations
.

.
We will use the first equation
.
=
.
=
.
We will move (-16) to the right
.
=
.
=
.
We found that "y" = "0"
.
We can now find "x", we need to replace "y" and "z" in one of the three original equations
.
y = 0
z = 4
.
x+3y+5z=20
y-4z=(-16)
3x-2y+9z=36
.
We will use the first equation, since it will be the easiest( we can't use the second equation)
.
=
.
=
.
=
.
We will move the "20" over to the right side
.
=
.

.
We found that "x" = "0", we now have all 3 variables, "x","y", and "z"
.
x = 0
y = 0
z = 4
.
We can check by replacing the letters with numbers in our third equation
.
=
.
=
.
= ( True)
.
x = 0
y = 0
z = 4
.
The solution set = (x,y,z), our solution set = (0,0,4)
.
Hope I helped, Levi
RELATED QUESTIONS
How to do the System of equations. It says solve the system of equations a)... (answered by MathLover1)

3x − 2y + z = −2 x + 3y − 4z = −5 2x − 3y... (answered by Alan3354)

Solve the system: 4x - 2y + 2z = 38 3y - 5z = -37 4z =... (answered by checkley75)

X+3Y+5Z+2W=2 -Y+3Z+4W=0 2X+Y+9Z+6W=-3... (answered by Solver92311)

Solve the following system of equations. ( If there are infinitely many solutions, enter... (answered by richwmiller)

SYSTEM OF 3 EQUATIONS WITH 3 UNKNOWNS FIND SOLUTION SET FOR THE FOLLOWING SYSTEM OF... (answered by pjalgeb,Theo)

Solve system of equations 2x+y+z=4 3x-y+4z=11... (answered by mananth)

solve the following system of equations using matrices. x+y-3z=3; -6x+5z=-6;... (answered by greenestamps)

solve system of equation by elimination 2x-y+z=7 3x+2y-2z=-7... (answered by nyc_function,Edwin McCravy)