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.
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
3 answers
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
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
or, for a more condensed presentation, type in your coefficients here and see all the details.
http://www.gregthatcher.com/Mathematics/GaussJordan.aspx
http://www.gregthatcher.com/Mathematics/GaussJordan.aspx