Question

Alg2 help (picture) Elimination

Answer 1

Nvm I get this one

Answer 2

2x + y = 9
x - 2z = -3
2y + 3z = 15

Is this the problem you need to solve by elimination?

Answer 3

#5

Answer 4

Nvm I actually need help in both...

Answer 5

2x + y = 9 ----- (1)
x - 2z = -3 ----- (2)
2y + 3z = 15 -----(3)

Multiply second equation by 2 and subtract it from the first equation:

2x + y = 9
2x - 4z = -6
Subtract
y + 4z = 15
Multiply the above equation by 2 and subtract it from equation 3

2y + 8z = 30
2y + 3z = 15
Subtract
5z = 15
z = 3
2y + 3z = 15. Substitute z = 3
2y + 9 = 15
2y = 15 - 9 = 6
y = 3
Equation 1) is 2x + y = 9. Substitute y = 3
2x + 3 = 9
2x = 9 - 3 = 6
x = 3

So x = 3, y = 3, z = 3

Answer 6

You can use the same method to solve the other equation:

2x - y + z = -4 ------- (1)
3x + y - 2z = 0 ------- (2)
3x - y = -4 ------- (3)

The last equation has only x and y and no z.
So try eliminating z using equations 1 and 2 first.
Let me know if you get stuck.

Answer 7

alright Ill try it now!

Answer 8

I got 7x - y = - 8

Answer 9

I multiplied 1st equation by 2

Answer 10

then eliminated with the second equation

Answer 11

Correct. So you have 7x - y = -8
and the third equation is: 3x - y = -4
Eliminate y from these two equations.

Answer 12

Ohh.. I just used that equation and made y = 7x + 8 then I substituted in 3x - y = -4

Answer 13

Is that correct too?

Answer 14

You can do that too.
But simply subtracting the two equations will eliminate y
7x - y = -8
3x - y = -4
subtract to get rid of y.

Answer 15

So far I got x is 3 and y is 13

Answer 16

z is 3

Answer 17

Not correct.

Answer 18

all of them?

Answer 19

In these types of problems if you get one of the values wrong then all other values will also be wrong because they depend on the the other values.

Answer 20

Okay so how would you do it?

Answer 21

Well, let us retrace your steps.
Earlier you had y = 7x + 8 and you said you substituted y in 3x - y = -4
Why don't you do that here and I will see what you get.

Answer 22

x is 3

Answer 23

No. Show me the step-by-step before you solved for x.
Start with y = 7x + 8 and substitute y in
3x - y = -4
Show me the step-by-step

Answer 24

\[2x - y + z = -4 \]

Answer 25

I multiplied it by 2

Answer 26

\[7x - y = -8\]

Answer 27

This is what I got, then I subtracted 7x from both sides and I got:

Answer 28

\[y = 7x +8\]

Answer 29

OK. Next step?

Answer 30

Alright so then I plugged in the Y for: \[3x - 7x + 8 = -4\]

Answer 31

3x - 7x is = -4

Answer 32

then minus 8 from both sides and -4x = -12..so now divide by -4 and x is 3

Answer 33

The mistake is in plugging in the y.

Answer 34

positive 7?

Answer 35

You had y = 7x + 8
Plug y in 3x - y = -4
3x - (7x + 8) = -4
3x -7x - 8 = -4 (you had +8 and that is the error)

Answer 36

why is 8 negative?

Answer 37

y = 7x + 8
When you put the above y in 3x - y you have to remember to put a parenthesis around y
so it should be 3x - ( substitute the y value here )
3x - (7x + 8)
Now remove the parentheses.
3x - 7x - 8

Answer 38

3x - y means you are subtracting y from 3x.
But if y is made up of two parts: 7x + 8 then each part of y has to be subtracted from 3x
so it becomes 3x - 7x - 8

Answer 39

ohh okay!

Answer 40

then how do I combine 3x - (7x+8) = -4 ?

Answer 41

what is -(a + b) if you remove the parenthesis?

Answer 42

-(a + b) = -a - b

Answer 43

x is 1?

Answer 44

so -(7x + 8) = -7x - 8

Answer 45

Not quite. X is not 1. Watch out for the signs

Answer 46

7x - 8?

Answer 47

You have 3x - (7x + 8) = -4
First get rid of the parenthesis. When ridding the parenthesis, the minus sign outside should be applied to each term inside the parenthesis.
So 3x - (7x + 8) = -4
becomes 3x - 7x - 8 = -4

Answer 48

i got 1 for x again

Answer 49

what is 3x - 7x ?

Answer 50

-4x

Answer 51

correct.
so -4x - 8 = -4
solve for x

Answer 52

plus 8 both sides

Answer 53

corrcet.

Answer 54

\[-4x = -4\]

Answer 55

then divide by -4

Answer 56

which is 1

Answer 57

-4x - 8 = -4
8 8 (add 8 to both sides of the equation)
-4x = 4 (not minus 4)
So x = ?

Answer 58

ohh!! -1 !!

Answer 59

Good!

Answer 60

What is y & z?

Answer 61

x = -1
y = 1
z = 1

Answer 62

check for z again.

Answer 63

z = -1

Answer 64

Yes! x = -1, y = 1, z = -1.

Once you solve these type of problems always substitute the values for x, y, z into the left hand side of the original 3 equations to see if you get the right hand side. That way you will know your answers are correct.

Answer 65

FINALLY!!!!

Answer 66

thank you for helping me!

Answer 67

No problem. Pay attention to the signs. Use parenthesis when substituting when there are many terms.

Good Luck!