Algebra-2

To solve the system of equations given:

1.( 5x - y + 3z = 22 )   (Equation 1)

2.( 2x + 4y - z = -22 )   (Equation 2)

3.( -x + 3y + 2z = 24 )   (Equation 3)

we will follow your instructions step by step.

 

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

Subtract Equation 3 from Equation 1:

(5x - y + 3z) - (-x + 3y + 2z) = 22 - 24

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

6x - 4y + z = -2 {Equation 4}

 

Add Equation 2 to Equation 4:

(6x - 4y + z) + (2x + 4y - z) = -2 + (-22)

6x - 4y + z + 2x + 4y - z = -24

8x = -24

x = -3 {Equation 5}

 

Step 2: Substitute ( x = -3 ) Back into the Equations to Find ( y ) and ( z )

Now that we have ( x ), we can substitute it back into either Equation 1 or Equation 2 to find ( y ) and ( z ).

Substituting ( x = -3 ) into Equation 1:

5(-3) - y + 3z = 22

-15 - y + 3z = 22

-y + 3z = 37