Question

Solve the system by substitution.
-x-y-z=-8
-4x+4y+5z=7
2x+2z=4
I need step by step help please!

Answer 1

First we should simplify each equation if possible. The first equation cn be simplified if we divide both sides by -1

The third equation can be simplified if we divide both sides by 2. The resulting system we get is:

x + y + z = 8
-4x + 4y + 5 = 7
x + z = 2

Answer 2

Next what we will do is pair the 1st and 3rd equation. Then pair the 1st and and 2nd equation to create two systems:

x + y + z = 8
x + z = 2


x + y + z = 8
-4x + 4y + 5 = 7

Are you with me so far?

Answer 3

Yes. So then we add them together right? @Hero

Answer 4

Well, hang on. We may need to add or subtract depending on how things are set up. What we are looking for is to eliminate variables

Answer 5

Now in this case, what we can do for the 1st system is subtract the 3rd equation from the first. If we do that we will get

y = 6

Let me know if you understand what I did there.

Answer 6

Yes I understand

Answer 7

Okay, so we already have y = 6
Let's insert y = 6 in to the second pair. If we do that we end up with
x + 6 + z = 8
-4x + 4(6) + 5z = 7

Answer 8

Okay now after that we will end up with

x + 6 + z = 8
-4x + 24 + 5z = 7

Answer 9

And then we will subtract 6 from both sides of the top equation
And subtract 24 from both sides of the bottom equation

Answer 10

We will end up with

x + z = 2
-4x + 5z = -17

Answer 11

So now we have a system of two equations which is relatively easy to solve.

Answer 12

okay

Answer 13

From here, we can simply multiply both sides of the top equation by 4 to get

4x + 4z = 8
-4x + 5z = -17

Answer 14

Now noticing that 4x and -4x are opposites, we can combine these equations together to eliminate x variable. When we do that we get:

9z = -9

Answer 15

And then dividing both sides by 9 we get:

z = -1

Answer 16

Let's use the simplest possible equation to find x.

Answer 17

x + z = 2

Answer 18

Since z = -1 we have

x - 1 = 2

Answer 19

So what does x equal?

Answer 20

3?

Answer 21

Correct. So what are the cooridinates of the solution point (x, y, z)?

Answer 22

3,6,-1

Answer 23

Yes correct.

Answer 24

The system is correct, but I made some errors above. There are places where I wrote 5 instead of 5z. I hope you recognize it.

Answer 25

Anyway, I will proceed to the other question.

Answer 26

yeah I saw it that you!