Can you help check if my answers for systems of liner equations are correct?

Question

If they aren't can you tell me the right answer and maybe even a short description of how you got there, thanks!

SOLVE EACH SYSTEM OF LINEAR EQUATIONS IF POSSIBLE.

2.
x=2
2x+3z=13
x-3y+z=-10

A: x=2, y=5, z=3

3.
x+z=5
-2x+y+z=-5
3x-2y-z=9

A: x=3, y=-1, z=2

4.
x-2y+3z=-3
2x-3y-z=7
3x+y-2z=6

A: x=(3/4), y=-1, z=-2

5.
x-2y+4z=-8
2x+2y-z=11
x+y-2z=10

A: x=4, y=0, z=-3

Answer 1

Except for Number 4 the rest are correct

The answers for number 4 are

x =1, y = -1 and z = -2

Checked them using Mathematica,

Answer 2

2.
x = 2

2(2) + 3z = 13
4 + 3z = 13
3z = 9
z = 3

2 - 3y + 3 = -10
3y = 15
y = 5

Answer: x = 2, y = 5, z = 3

3.
x + z = 5
x = 5 - z

-2(5 - z) + y + z = - 5
- 10 + 2z + y + z = - 5
y = 5 - 3z

3(5 - z) - 2(5 - 3z) - z = 9
15 - 3z - 10 + 6z - z = 9
2z = 4
z = 2

x = 5 - 2
x = 3

y = 5 - 3(2)
y = 5 - 6
y = - 1

Answer: x = 3, y = - 1, z = 2

4.
x - 2y + 3z = - 3
x = 2y - 3z - 3

2(2y - 3z - 3) - 3y - z = 7
4y - 6z - 6 - 3y - z = 7
y = 7z + 13

x = 2(7z + 13) - 3z - 3
x = 14z + 26 - 3z - 3
x = 11z + 23

3(11z + 23) + (7z + 13) - 2z = 6
33z + 69 + 7z + 13 - 2z = 6
38z = - 76
z = - 2

x = 11(- 2) + 23
x = - 22 + 23
x = 1

y = 7(- 2) + 13
y = - 14 + 13
y = - 1

Answer: x = 1, y = - 1, z = - 2

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

2(2y - 4z - 8) + 2y - z = 11
4y - 8z - 16 + 2y - z = 11
6y = 9z + 27
2y = 3z + 9
y = 1.5z + 4.5

x = 2(1.5z + 4.5) - 4z - 8
x = 3z + 9 - 4z - 8
x = 1 - z

(1 - z) - 2z = 10
1 - z - 2z = 10
3z = - 9
z = - 3

x = 1 - (- 3)
x = 1 + 3
x = 4

y = 1.5(- 3) + 4.5
y = - 4.5 + 4.5
y = 0

Answer: x = 4, y = 0, z = - 3

Answer 3

2.
x = 2

2x + 3z = 13
2(2) + 3z = 13
4 + 3z = 13
3z = 9
z = 3

x - 3y + z = -10

2 - 3y + 3 = - 10
-3y + 5 = - 10
-3y = - 15
y = 5

3.
x + z = 5
x = 5 - z

-2x+y+z=-5
-2(5 - z) + y + z = - 5
- 10 + 2z + y + z = - 5
y + 3z = 5
2y + 6z = 10

3x-2y-z=9
3(5 - z) - 2y - z = 9
15 - 3z - 2y - z = 9
-2y - 4z = - 6

2y + 6z = 10
-2y - 4z = - 6
- - - - - - - - - -
2z = 4
z = 2

x = 5 - 2
x = 3

3(3) - 2y - 2 = 9
9 - 2y - 2 = 9
-2y = 2
y = -1

4.
1) x-2y+3z=-3
2) 2x-3y-z=7
3) 3x+y-2z=6

On this one I eliminated x by multiplying eq 1 by -2 and adding it to eq 2 and then multiplying eq 1 by -3 and adding it to eq 3

Solving that set I got z = -2 and y = -1

1) x-2y+3z=-3
x - 2(-1) + 3(-2) = - 3
x + 2 - 6 = - 3
x - 4 = - 3
x = 1 {we disagree here}

5.
x-2y+4z=-8
2x+2y-z=11
x+y-2z=10

I agree with your answer on this one

Answer 4

4. x = 1

Answer 5

in case you have gained a cost for all the variables, only plug them lower back into the set of equations and confirm the solutions upload up. to illustrate in case you had that 10x + 12y = 22 and additionally you may gained a cost of a million for x and a couple of for y, you may see that 10*a million + 12*2 does not equivalent 22, so your calculation could be incorrect. attempt lower back till at last you get the two = a million.

Answer 6

They were all computer-checked.
2,3, and 5 are correct.
Problem 4: x=1 y=-1 z=-2

Answer 7

Ok go

x=2
2x+3z=13
x-3y+z=-10
-------------------

If "x=2" then
2x+3z=13
4 +3z = 13
3z = 9
z = 3
-------¦

If "x=2" and "z=3" then
x-3y+z= -10
2-3y+3= -10
-3y = -15
y = 5
--------¦

Try your work x=2; y=5; z=3

x=2
2 =2

2x+3z=13
4+ 9 = 13
13 = 13

x-3y+z=-10
2-15 +3 =-10
-10 = -10

______________________________________________

x+z=5
-2x+y+z=-5
3x-2y-z=9
-----------------

If "z = 5-x" then
-2x+y+z=-5
-2x+y+(5-x)=-5
-2x+y+5-x =-5
-3x +y =-10......(a)
-------------------

If "z = 5-x" then
3x-2y-z=9
3x-2y-5+x=9
4x -2y =14.......(b)
--------------------

-3x +y =-10...(a)
4x -2y =14....(b)
--------------------

2¦ -3x +y =-10
..¦4x -2y =14
---------------------

-6x +2y =-20
.4x -2y =14
-------------------
-2x.......=-6
...x=3

.4x -2y =14
12 - 2y=14
-2y =2
y =-1

If "x=3" then
x+z=5
3+z =5
z=2

Try your work "x=3"; "y=-1"; "z=2"

x+z=5
3 +2=5
5=5

-2x+y+z=-5
-6-1+2=-5
-5=-5

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

x-2y+3z=-3.....(1)
2x-3y-z=7.......(2)
3x+y-2z=6......(3)
-----------------

x-2y+3z=-3....(1)
2x-3y-z=7......(2)
-----------------
-2¦ x-2y+3z=-3
...¦2x-3y-z=7
---------------------
-2x+4y-6z=6
.2x-3y-z=7
--------------------
......y-7z=13....(a)
------------------

2x-3y-z=7.....(2)
3x+y-2z=6....(3)
----------------
.3¦ 2x-3y-z=7
-2¦ 3x+y-2z=6
-------------------
.6x-9y-3z=21
-6x-2y+4z=-12
--------------------
....-11y+z=9....(b)
------------------

......y-7z=13....(a)
-11y+ z=9......(b)
-----------------------

....¦ y -7z= 13
7 ¦ -11y+ z=9
-----------------------
......y-7z =13
-77y+7z=63
---------------------
-76y =76
y= -1

y-7z=13
-1-7z=13
-7z=14
z=-2

x-2y+3z=-3
x+2-6=-3
x=1


Try your work "x = 1"; "y =-1"; "z= -2"

x-2y+3z=-3
1+2-6=-3
-3=-3

2x-3y-z=7
2+3+2=7
7=7

3x+y-2z=6
3-1+4=6
6=6

_________________________________________

x-2y+4z=-8
2x+2y-z=11
x+y-2z=10
--------------------P(4,0,-3)

And now check

x-2y+4z=-8
4-0-12=-8
-8=-8

2x+2y-z=11
8+0+3=11
11=11

x+y-2z=10
4+0+6=10
10= 10


Bye-bye!

Answer 8

You can do it yourself easily: put the solution in the equations and if you have the same numbers on both sides, the solution is correct. I have done that for your first problem and the solution is correct.

Answer 9

you already have the answers!

they are called simultaneous linear equations in 3 variables, by the way

Answer 10

No. But I can correct your spelling. Liner is spelled linear.