Question

How do you do this linear equation with three variables?:

{-2x+3y-5z=3
5x-7y+12z=-8
X-y+2z=-2

Answer 1

Find the value of one variable x, y or z from any one equation and then put it in other two equations, you will get two equations containing only two variables, then solve this further to find the two variables first..

Answer 2

Suppose we find y from Third equation:

\[x - y + 2z = -2 \implies y = x + 2z + 2\]

Now put this value of y in other two equation one by one..

Answer 3

\[-2x+3y-5z=3 \implies -2x + 3(x + 2z + 2) - 5z = 3\]
\[-2x + 3x + 6z + 6 = 3 \implies x + 6z = -3\]

Answer 4

Similarly in second one:
\[ 5x-7y+12z=-8 \implies 5x - 7(x + 2z + 2) + 12z = -8\]
\[5x - 7x - 14z - 14= -8 \implies -2x - 14z = 6 \implies x + 7z = -3\]

Answer 5

Now you have got two equations:
\[x + 6z = -3\]
\[x + 7z = -3\]

Solve to find x and z..

Answer 6

Can you do this @K.marie ??

Answer 7

Yes thank you

Answer 8

Solve it and post your answer so that I can check..

Answer 9

X=-39 y=-49 z=-6

Answer 10

How??

No..

Just solve those two equations..

Answer 11

Oh then z=-6 and when I plug that back in I get x=-39

Answer 12

How z = -6 ??

Answer 13

Multiply x+6z=-3 by -1 and add to x+7z=-3 to get z=-6

Answer 14

By multiplying you will get:

-x - 6x = 3
x + 7z = -3

Now add them what you got?

Answer 15

X gets cancelled and the 6 is actually a z so that becomes one z

Answer 16

Yes that becomes one z..

So what is -3 + 3 = ??

Answer 17

ON RHS what will be the result??

Answer 18

0 so it's a no solution

Answer 19

Hey, it is having solution..

Answer 20

But here z = 0, now find x and y..

Answer 21

Oh okay

Answer 22

X=-3 and y=-1

Answer 23

Yep, now you are right..

So, x = -3, y = -1 and z = 0..