Solve the following set of equation by elimination method?

Question

Solve the following set of equation by elimination method

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

and
solve by substution
4x-y-z = 4
2x+5y+3z = -3
3x+2y-4z = -2

Answer 1

This is the last one I'll do before going to bed. Equation numbers in parentheses.

3x - 4y - z = 1 (1)
x + 2y - 3z = -2 (2)
4x + 3y - 2z = -1 (3)
6x - 8y - 2z = 2 (1)
-2x + 11y = -3 (3 - 1 ==> 4)
2x + 4y - 6z = -4 (2)
12x + 9y - 6z = -3 (3)
10x + 5y = 1 (3 - 2 ==> 5)
-10x + 55y = -15 (4)
60y = -14 (5 + 4 ==> 6)
y = - 7/30 (6) Answer
10x - 35/30 = 1 (6 ==> 5)
x = 65/300 = 13/60 (5) Answer
39/60 + 28/30 - z = 1 (5, 6 ==> 1)
z = (39 + 56 - 60)/60 = 35/60 = 7/12 (1) Answer

The solution is x = 13/60, y = -7/30, z = 7/12

4x - y - z = 4 (1)
2x + 5y + 3z = -3 (2)
3x + 2y - 4z = -2 (3)
z = 4x - y - 4 (1)
2x + 5y + 12x -3y -12 = -3 (1, 2 ==> 4)
14x +2y = 9 (4)
3x + 2y -16x + 4y + 16 = -2 (1, 3 ==> 5)
-13x + 6y = -18 (5)
2y = 9 - 14x (4)
6y = 27 - 42x (4)
-13x + 27 - 42x = -18 (4, 5 ==> 6)
45 = 55x (6)
x = 9/11 (6) Answer
2y = 9 - 126/11 = - 27/11 (6 ==> 4)
y = - 27/22 (4) Answer
z = 36/11 + 27/22 - 4 (6, 4 ==> 1)
z = (72 + 27 - 88)/22 = 1/2 (1) Answer

The solution is x = 9/11, y = -27/22, z = 1/2

Answer 2

As I keep in mind the removal approach is carried out via removing between the variables via substitution. Taking #a million 3x - y = 2 3x - 2 = y Now replace this equation for y in Equation #2 6x - 2(3x -2) = 4 6x - 6x + 4 = 4 4 = 4 via ending up without variables this tells you that any mix of x and y that satisfies between the equations will fulfill the different. this might additionally be considered via rearranging #2 6x - 2y = 4 6x - 4 = 2y then divide via 2 3x -2 = y that's a similar as a results of fact the 1st equation. x = a million and y = a million will artwork, yet so will an countless sort of alternative solutions see you later as x = (y + 2)/3

Answer 3

to start you off: the second equation (set 1) looks like the easiest to work with,,,,M(-3) and add to the first equation (this eliminates the 3x) then M(-4) and add to the last equation (again eliminates the x term). Then move to the next variable (y) and do similar operations to clear out the y terms....then do same with z ...good luck !


By substitution? Second set of equations: solve the first equation for either y or z . if y then you get y = 4x-y-4 substitute this into the last equation (or the second equation) and continue...solve next for one of the other variables (other than the one you used first)...this substitution process can be tricky so be careful and include steps slowly.

Good luck !

You are solving by different methods so you will see that in certain cases one method will work quicker than another.
Be sure to check your final answer in the orginial equations.

Answer 4

-3(3x-4y-z=1)
x+2y-3z=-2
.......................
-8x + 14 y = -5

-2(3x-4y-z=1)
4x+3y-2z= -1
.....................
-2x + 11y = -3

2(8x + 14y = -5)
8(-2x + 11y = -3)
............................
116y = -34
y = -34/116
x = -13/116
z = ? Damn I don't think I did that right lol.

Answer 5

wow there was a time I knew how to do this. Frustrating.