solve this system of equations?

Question

4x-3y+2z=-9
-5x+y+3z=19.5
-x+2y-z=1.5

so, by adding the first 2 equations, i think im supposed to eliminate y, and by adding the last 2 equations, i eliminate y again. that way i can eliminate x or z by adding my 2 new equations, right?

Answer 1

4x - 3y + 2z = - 9
- 15x + 3y + 9z = 58.5----ADD

- 11x + 11z = 49.5

10x - 2y - 6z = - 39
-x + 2y - z = 1.5-------ADD

9x - 7z = - 37.5
-x + z = 4.5

9x - 7z = - 37.5
-9x + 9z = 40.5-----ADD

2z = 3
z = 1.5

-x + 1.5 = 4.5
x = - 3

15 + y + 4.5 = 19.5
y = 0

Answer is x = - 3 , y = 0, z = 1.5

Answer 2

4x - 3y + 2z = -9 (eq.1)
-5x + y + 3z = 19.5 (eq.2)
-x + 2y - z = 1.5 (eq.3)

1) Multiply eq.3 by 4
4(-x +2y - z = 1.5)
-4x + 8y - 4z = 6 (Eq.4)
2) Add eq. 1 and eq.4
4x - 3y + 2z = - 9
-4x + 8y - 4z = 6
______________
5y - 2z = -3 (eq.5)
3) Multiply eq. 3 by -5
-5(-x + 2y - z = 1.5)
5x - 10y + 5x = -7.5 (eq. 6)
4) Add eq. 6 and eq. 2
5x - 10y + 5x = -7.5
-5x + y + 3z = 19.5
_________________
-9y + 8z = 12 (eq. 7)
5) Multiply eq. 3 by 4
4(5y - 2z = -3)
20y - 8z = -12 (eq.8)
6) Add eq. 8 and eq. 7
20y - 8z = -12
-9y + 8z = 12
_____________
11y = 0
y = 0/11
y = 0 ===> value of y
7) Substitute value of y to either eq. 5 or eq. 7

5(0) - 2z = -3 (eq. 5)
0 -2z = -3
-2z/-2 = -3/-2
z = 3/2 or 1.5 ==> value of z
8) Subtitute value of y = 0 and z = 1.5 to eq. 1, 2 or 3

4x -3(0) + 2(1.5) = -9 (eq. 1)
4x - 0 + 3 = - 9
4x = - 9 - 3
4x = -12
4x/4 = -12/4
x = -3 ==> value of x

x = - 3
y = 0
z = 1.5
To check:
Substitute the value of x = -3, y = 0 and z = 1.5 to either eq. 1, 2 or 3

-5(-3) + 0 + 3(1.5) = 19.5 (eq. 2)
15 + 0 + 4.5 = 19.5
19.5 = 19.5

Your immediate purpose is to eliminate a term (or variable or unknown) so that you will come out with only 2 terms, which is easier to evaluate. You can either multiply or divide, add or subtract. Any operation done in the right must also be done in the left side.

Answer 3

Solve this system of equations?
4x-3y+2z=-9.....................(1)
-5x+y+3z=19.5...................(2)
-x+2y-z=1.5 .....................(3).
(1)+2*(3)gives: 2x+y=12.................................(4)
(2+3*(3) gives:-8x+7y=24.........................(5)
4*(4+(5 gives:))11y=72
so y=72/11, 2x=12-72/11 =60/11, x=30/11
z=-x+2y-1.5=30/11+144/11-1.5=174/11-1.5=15.81-1.5=14.31

Answer 4

4x-3y+2z=-9 (I)
-5x+y+3z=19.5 (II)
-x+2y-z=1.5 (III)
Solving:
Eliminating:
-15x + 3y + 9z = 58.5 (I)
4x - 3y + 2z = -9 (II)
--------------------------
-11x + 11z = 49.5

-5x + y + 3z = 19.5 (II)
-x + 2y - z = 1.5 (III)

10x - 2y - 6z = -39
-x + 2y -z = 1.5
-------------------------
9x - 7z = -37.5

9x - 7z = -37.5 (*11)
-11x + 11z = 49.5 (*9)

99x - 77z = -412.5
-99x +99z = 445.5
--------------------------
22z = 33
z = 3/2 = 1.5

-x + 2y -1.5 = 1.5(iii)
4x - 3y + 2(1.5) = -9 (I)

So,
-x + 2y - 1.5 = 1.5
-5x + y + 3(1.5) = 19.5
------------------------
-6x + 3y +3 = 21
-6x + 3y = 21-3
-6x = 3y = 18

4x - 3y + 2(1.5) = -9
4x -3y + 3 = -9
4x + 3y = -9 - 3
4x + 3y = -12

-6x + 3y = 18
4x - 3y = -12
-------------------
-2x = 6
x = 6/-2
x = -3

-x + 2y - z = 1.5
-(-3) + 2y - 1.5 = 1.5
2y = 1.5 + 1.5 - 3
2y = 0
y = 0
Solution:
{(x = -3; y = 0; z = 1.5)}
:>::

Answer 5

x = -3
y = 0
z = 1.5

consider adding eq. 1 and 2 and eq 2 and 3
then start to work on solving it.. don't worry it's easy! :)