Algebra-2

Given System of Equations

1.( 2x - y = 2 ) (Equation 1)

2.( x + 4y + 5z = 6 )  (Equation 2)

3.( 5x + 2y - 5z = 0 ) (Equation 3)

 

Step 1: Add Equations 2 and 3

Adding Equations 2 and 3 gives:

(x + 4y + 5z) + (5x + 2y - 5z) = 6 + 0

x + 5x + 4y + 2y + 5z - 5z = 6

6x + 6y = 6

 

Step 2: Simplify the Equation

Now, we can simplify this equation:

6x + 6y = 6

Divide the entire equation by 6:

x + y = 1 (Equation 4)

 

Step 3: Solve the System

Now we have:

( 2x - y = 2 ) (Equation 1)

( x + y = 1 ) (Equation 4)

 

Step 4: Solve for (y)

From Equation 4, we can express ( y ):