Algebra-2

Given System of Equations

1.( 4x - y + z = -4 )  (Equation 1)

2.( -x + 3y - 2z = 10 )  (Equation 2)

3.( 2x + y + 3z = -4 )   (Equation 3)

 

Step 1: Subtract Equation 1 from Equation 2 and Add Equation 3 to Eliminate ( z )

Subtract Equation 1 from Equation 2:

(-x + 3y - 2z) - (4x - y + z) = 10 - (-4)

-x + 3y - 2z - 4x + y - z = 10 + 4

-5x + 4y - 3z = 14 {Equation 4}

 

Now add Equation 3 to Equation 4:

(-5x + 4y - 3z) + (2x + y + 3z) = 14 + (-4)

-5x + 4y - 3z + 2x + y + 3z = 10

-3x + 5y = 10{Equation 5}

 

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

Multiply Equation 1 by 2:

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

8x - 2y + 2z = -8 {Equation 6}

 

Now add Equation 2 to Equation 6:

(8x - 2y + 2z) + (-x + 3y - 2z) = -8 + 10

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

7x + y = 2 {Equation 7}

 

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