Algebra-2

To solve the system of equations:

1.(3x + y - 2z = -31)  (Equation 1)

2.(x - 3y + 4z = 11)   (Equation 2)

3.(2x + 3y + z = -2)    (Equation 3)

 

Step 1: Multiply Equation 1 by 2 and add Equation 2

First, we multiply Equation 1 by 2:

2(3x + y - 2z) = 2(-31)

6x + 2y - 4z = -62 (Equation 4)

 

Now, we add Equation 4 to Equation 2:

(6x + 2y - 4z) + (x - 3y + 4z) = -62 + 11

6x + x + 2y - 3y - 4z + 4z = -62 + 11

7x - y = -51

7x - y = -51(Equation 5)

 

Step 2: Multiply Equation 3 by 2 and add Equation 1

Next, we multiply Equation 3 by 2:

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

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

 

Now, we add Equation 6 to Equation 1:

(4x + 6y + 2z) + (3x + y - 2z) = -4 - 31

4x + 3x + 6y + y + 2z - 2z = -4 - 31

7x + 7y = -35

x + y = -5 (Equation 7)

 

Step 3: Solve the system of equations

Now we have the simplified system of equations:

(7x - y = -51) (Equation 5)

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