solve the system of equations

Question

x - y + z = -7

x + y + z =1

x + y - z = 9

Answer 1

Also but I think that I am going too far the solution by linear algebra may be used having the extended matrix and the determinant of the system and solving for every one of the variables. I think that this goes out of the subject.

Answer 2

x - y + z = -7
x + y + z =1
x + y - z = 9

Second equation minus first equation

0+2y+0=8       y=4

Second equation minus third equation

0+0+2z=-8      z=-4

First equation plus third equation

2x+0+0=2       x=1

There is virtue in staring prior to calculation.

Answer 3

Jimmie, there are different ways to go about this, but let's try combining equations.  Let's add the first and third:

 

    x - y + z = -7

+  x + y - z  = 9

_______________

 

   2x            = 2

 

So, x = 1

 

Now, let's add the first two:

 

   x - y +  z = -7

+ x + y + z =  1

______________

 

  2x        + 2z = -6  

 

Subsitute in our x = 1

 

2 (1) + 2z = -6

 

2 + 2z = -6

 

So, z = -4

 

Plug in your x and z values into any of the equations to find the value for y.

Answer 4

Jimmie,

 

We have 3 equations with 3 unknowns, so we should be able to solve.

 

(1)  x - y +z = -7

 

(2)  x + y +z = 1

 

(3)  x + y - z = 9

 

First let's add #'s (1) & (2)

 

This gives 2·x + 0 + 2·z = -7 + 1 = -6, which simplifies to:

 

(4) x + z = -3

 

Now subtract (3) from (2) and get 0 + 0 + 2·z = -8,

 

so z = -4

 

Substitute in (4) directly above and x -4 = -3 and x = -3 + 4 = 1

 

We now have x =1 & z = -4

 

We substitute these results into any of (1), (2), or (3) above.

 

With eqn (2) then 1 + y -4 = 1 and rearranging gives y -3 = 1, so y = 4

 

now:

 

x = 1

y = 4

z = -4