2x+y+2z=7, 2x-y+2z=1, 5x+y+5z=13

y = 3

x = 2 - z

Step-by-step explanation:

We have the system:

2*x+y+2*z=7

2*x-y+2*z=1

5*x+y+5*z=13

In the first and second equations we have the term (2*x + 2*z) = A

Then we can rewrite the first two equations as:

A + y = 7

A - y = 1

isolating A in the first equation, we get:

A = 1 + y

Now we replace this in the other equation:

(1 + y) + y = 7

1 + 2*y = 7

2*y = 6

y = 3.

then:

A + y = 7

A + 3 = 7

A = 7- 3 = 4

A = 2*x + 2*z  = 4.

Now let's go to the third equation:

(5*x + 5*z) + y = 13

we can rewrite the thing inside the parentheses as:

(5/2)*(2*x + 2*y) + y = 13

And we know that:

2*x + 2*z = 4

y = 3

then this can be written as:

(5/2)*(4) + 3 = 5*2 + 3 = 13

Then we can conclude that:

y = 3

2*z + 2*x = 4

2*(z + x) = 4

(z + x) = 4/2 = 2

x = 2 - z

Notice that the solution is not only a point, we have infinite solutions for this problem.

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