Algebra-2

System of Equations

( x + 2y + z = 5 )  (Equation 1)  

( 2x - y = 1 )  (Equation 2)  

( z - 4y = -2 ) (Equation 3)  

Step 1: Express ( z ) in terms of ( y ) from Equation 3

First, let’s express ( z ) from Equation 3:

z = 4y - 2 (Equation 4)

Step 2: Substitute ( z ) in Equation 1

Now, substitute Equation 4 into Equation 1:

x + 2y + (4y - 2) = 5

x + 2y + 4y - 2 = 5

Combine like terms:

x + 6y - 2 = 5

Adding 2 to both sides:

x + 6y = 7 (Equation 5)

Step 3: Now we have two equations (Equation 2 and Equation 5)

Now we can work with the following two equations:

( x + 6y = 7 )  (Equation 5)  

( 2x - y = 1 )   (Equat...