Algebra-2

To find the solution for the system of equations given:

4x + y + z = 10

y + 2z = 8

x - z = 2  

we can solve this step-by-step.

Step 1: Solve the third equation for (z)

From the third equation:

x - z = 2
z = x - 2

Step 2: Substitute (z) into the other equations

Now we will substitute (z = x - 2) into the first and second equations.

Substitute into the second equation:

y + 2z = 8

Substituting (z):

y + 2(x - 2) = 8

Expanding gives:

y + 2x - 4 = 8

Rearranging:

y + 2x = 12
y = 12 - 2x

Substitute into the first equation:

Now substitute (z = x - 2) into the first equation:

4x + y + z = 10

Substituting (y) and (z):...