Algebra-2

Given System of Equations

1.( 3x + 5y - z = -12 )   (Equation 1)

2.( x - 4y + 2z = 9 )       (Equation 2)

3.( -2x + 3y + z = 17 )     (Equation 3)

 

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

Add Equation 1 and Equation 3:

(3x + 5y - z) + (-2x + 3y + z) = -12 + 17

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

x + 8y = 5 {Equation 4}

 

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

Multiply Equation 1 by 2:

2(3x + 5y - z) = 2(-12)

6x + 10y - 2z = -24 {Equation 5}

 

Now add Equation 2 to Equation 5:

(6x + 10y - 2z) + (x - 4y + 2z) = -24 + 9

6x + 10y - 2z + x - 4y + 2z = -15

7x + 6y = -15 {Equation 6}

 

Summary of New Equations

Now we have two new equations, Equation 4 and Equation 6:

Equation 4: ( x + 8y = 5 )

Equation 6: ( 7x + 6y = -15 )

 

Step 3: Solve for ( y ) and ( x )

From Equation 4, expr...