Question

Solve by elimination
-2x+2y+3z=0
-2x-y+z=-3
2x+3y+3z=5

Please help. I have 5 pages and 3 hours spent and found the question on Google, but the calculations did not add up correctly.
Thank you

Answer 1

Step 1: Multiply first equation by −1 and add the result to the second equation. The result is:

-2x+2y+3z=0
-3y-2z=-3
2x+3y+3z=5

Step 2: Multiply first equation by 1 and add the result to the third equation. The result is:

-2x+2y+3z=0
-3y-2z=-3
5y+6z=5

Step 3: Multiply second equation by 3 and add the result to the third equation. The result is:
-2x+2y+3z=0
-3y-2z=-3
-4y=-4

Step 4: solve for y.
-4y=-4
y=1

Step 5: plug y in and solve for z.
-3y-2z=-3
-2z=0
z=0

Step 6: solve for x by substituting y=1 and z=0 into the first equation.

Answer 2

Multiply first equation by − 1

The result: 2 x - 2 y - 3 z = 0

Add the result to the second equation

2 x - 2 y - 3 z = 0
+
- 2 x - y + z = - 3
_______________

0 - 3 y - 2 z = - 3

- 3 y - 2 z = - 3

Add the first equation to the third equation

- 2 x + 2 y + 3 z = 0
+
2 x + 3 y + 3 z = 5
_________________

0 + 5 y + 6 z = 5

5 y + 6 z = 5

Now you have system of two equatios:

- 3 y - 2 z = - 3

5 y + 6 z = 5


- 3 y - 2 z = - 3 Multiply both sides by 3

- 9 y - 6 z = - 9


- 9 y - 6 z = - 9
+
5 y + 6 z = 5
____________
4 y + 0 = 4

4 y = 4 Divide both sides by 4

y = 4 / 4

y = 1

Replace y = 1 in equation:

- 3 y - 2 z = - 3

- 3 * 1 - 2 z = 3

- 3 - 2 z = - 3 Add 3 to both sides

- 3 - 2 z + 3 = - 3 + 3

2 z = 0 Divide both sides by 2

z = 0


Replace y = 1 and z = 0 in equation:

2 x + 3 y + 3 z = 5

2 x + 3 * 1 + 3 * 0 = 5

2 x + 3 = 5 Subtract 3 to both sides

2 x + 3 - 3 = 5 - 3

2 x = 2 Divide both sides by 2

x = 2 / 2

x = 1


The solutions are x = 1 , y = 1 , z = 0

Answer 3

or, for a more condensed presentation, type in your coefficients here and see all the details.

http://www.gregthatcher.com/Mathematics/GaussJordan.aspx