SOLUTION: Could you please help me solve the system of equations? 3x+3y+z=5 x-3y+2z=-13 8x-2y+3z=-8

Question 151298: Could you please help me solve the system of equations?
3x+3y+z=5
x-3y+2z=-13
8x-2y+3z=-8
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Add equations 1 and 2. Let's call the result equation 4:

+
-----------------

Equation 4:

Multiply both sides of equation 1 by 2

Multiply. Let's call this equation 5

-------

Multiply both sides of equation 3 by 3

Multiply. Let's call this equation 6

Now add equations 5 and 6. Let's call the result equation 7:

+
-------------------

Equation 7:

===================================

So we now have the two equations equation 4 and equation 7:

equation 4:
equation 7:

Start with the given system of equations:

Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for z.

So let's isolate z in the first equation

Start with the first equation

Subtract from both sides

Rearrange the equation

Divide both sides by

Break up the fraction

Reduce

---------------------

Since , we can now replace each in the second equation with to solve for

Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.

Distribute to

Multiply

Multiply both sides by the LCM of 3. This will eliminate the fractions (note: if you need help with finding the LCM, check out this solver)

Distribute and multiply the LCM to each side

Combine like terms on the left side

Add 88 to both sides

Combine like terms on the right side

Divide both sides by 46 to isolate x

Divide

So the first part of our answer is:

Since we know that we can plug it into the equation (remember we previously solved for in the first equation).

Start with the equation where was previously isolated.

Plug in

Multiply

Combine like terms and reduce. (note: if you need help with fractions, check out this solver)

So the third part of our answer is:

Go back to the first equation

Plug in and

Multiply

Combine like terms.

Add to both sides.

Combine like terms on the right side.

Divide both sides by to isolate .

Reduce.

So the second part of the answer is

-----------------Summary------------------------------

So our answers are:

, , and

They form the point (1,2,-4)

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