Algebra-2

Given System of Equations

1.( 2x + 3y - z = 14 )   (Equation 1)

2.( -x + 2y + 3z = 9 )    (Equation 2)

3.( 3x - 4y + 2z = 30 )    (Equation 3)

 

Step 1: Subtract Equation 3 from Equation 2 and Add Equation 1

Subtract Equation 3 from Equation 2:

(-x + 2y + 3z) - (3x - 4y + 2z) = 9 - 30

-x + 2y + 3z - 3x + 4y - 2z = -21

-4x + 6y + z = -21 {Equation 4}

 

Add Equation 1 to Equation 4:

(-4x + 6y + z) + (2x + 3y - z) = -21 + 14

-4x + 2x + 6y + 3y + z - z = -7

-2x + 9y = -7

2x - 9y = 7 {Equation 5}

 

Step 2: Multiply Equation 1 by 3 and Add Equation 2 to Eliminate ( z )

Multiply Equation 1 by 3:

3(2x + 3y - z) = 3(14)

6x + 9y - 3z = 42 {Equation 6}

 

Add Equation 2 to Equation 6:

(6x + 9y - 3z) + (-x + 2y + 3z) = 42 + 9

6x - x + 9y + 2y - 3z + 3z = 51

5x + 11y = 51 {Equation 7}

 

Step 3: Multiply Equation 5 by 5 and Equation 7 by 2 to Eliminate ( x )...