Algebra-2

Given System of Equations

1.( x + y + z = -1 )   (Equation 1)

2.( 2x - y + 3z = -7 ) (Equation 2)

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

 

Step 1: Combine Equation 1 and Equation 3, then Subtract Equation 2 to Eliminate ( z )

Add Equation 1 and Equation 3:

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

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

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

 

Now subtract Equation 2 from Equation 4:

(4x + 5y + 3z) - (2x - y + 3z) = -3 - (-7)

4x + 5y + 3z - 2x + y - 3z = -3 + 7

2x + 6y = 4

x + 3y = 2 {Equation 5}

 

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

Multiply Equation 1 by 3:

3(x + y + z) = 3(-1)

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

 

Now subtract Equation 2 from Equation 6:

(3x + 3y + 3z) - (2x - y + 3z) = -3 - (-7)

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

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