KKV-842 the steps to solve the equations one by one based on the given options:
### Step 1: Select the simplest equation from the given system
The first equation is ( z - y = 0 ), which can be rewritten as ( z = y ). This equation is simple, select it first.
### Step 2: Substitute the value of ( z ) from the first equation into the other equations
Now, substitute ( z = y ) into the third and fourth equations to eliminate ( z ):
1. Substitute ( z = y ) into ( y - x = 0 ):
[ y - x = 0 ]
[ x = y ]
2. Substitute ( z = y ) into ( y - w = 0 ):
[ y - w = 0 ]
[ w = y ]
3. Substitute ( z = y ) into ( w - x = 0 ):
[ w - x = 0 ]
[ w = x ]
Since ( x = y ), ( w = y )
### Step 3: Determine the value of ( y )
From the second equation ( z - w = 0 ), since ( z = y ) and ( w = y ):
[ y - w = 0 ]
[ y - y = 0 ]
[ 0 = 0 ]
This gives us no information about ( y ), so we can set ( y ) to any real number ( a ).
### Step 4: Determine the values of ( x, z, w )
Since ( x = y ), ( z = y ), and ( w = y ):
[ x = y ]
[ z = y ]
[ w = y ]
So, all variables are equal to ( y ), which is equal to ( a ).
### Step 5: Write the final solution
[ x = a ]
[ y = a ]
[ z = a ]
[ w = a ]
31 Mar 2015