Algebra-2

Given System of Equations

1. x + 3y - 4z = 9  (Equation 1)

2. 2x - 2y + z = 1   (Equation 2)

3. 4x + y + 5z = 4   (Equation 3)

 

Step 1: Subtract Equation 2 from Equation 1 and add Equation 3 to eliminate z:

Subtract Equation 2 from Equation 1:

(x + 3y - 4z) - (2x - 2y + z) = 9 - 1

x + 3y - 4z - 2x + 2y - z = 8

-x + 5y - 5z = 8 (Equation 4)

 

Now add Equation 3 to Equation 4:

(-x + 5y - 5z) + (4x + y + 5z) = 8 + 4

-x + 5y - 5z + 4x + y + 5z = 12

3x + 6y = 12

x + 2y = 4 (Equation 5)

 

Step 2: Multiply Equation 2 by 4 and add to Equation 1 to eliminate z

Multiply Equation 2 by 4:

4(2x - 2y + z) = 4(1)

8x - 8y + 4z = 4 (Equation 6)

 

Now add Equation 1 to Equation 6:

(x + 3y - 4z) + (8x - 8y + 4z) = 9 + 4

x + 3y - 4z + 8x - 8y + 4z = 13

9x - 5y = 13 (Equation 7)

 

Step 3: Summary of the new equations

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