Algebra-2

To solve the system of equations:

1.(2x + 5y - 3z = 0)  (Equation 1)

2.(3x - 2y + z = 6)   (Equation 2)

3.(x + 3y + 4z = 46)   (Equation 3)

 

Step 1: Eliminate (z) from Equations 1 and 2

Multiply Equation 2 by 3:

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

9x - 6y + 3z = 18 (Equation 4)

 

Now, we add Equation 1 to Equation 4 to eliminate (z):

(2x + 5y - 3z) + (9x - 6y + 3z) = 0 + 18

2x + 9x + 5y - 6y - 3z + 3z = 18

11x - y = 18 (Equation 5)

 

Step 2: Eliminate (z) from Equations 2 and 3

Multiply Equation 2 by 4:

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

12x - 8y + 4z = 24 (Equation 6)

 

Now, we subtract Equation 3 from Equation 6 to eliminate (z):

(12x - 8y + 4z) - (x + 3y + 4z) = 24 - 46

12x - x - 8y - 3y + 4z - 4z = -22

11x - 11y = -22

 

Dividing through by 11 gives:

x - y = -2 (Equation 7)

 

Step 3: Solve the simplified system of equations

Now we ha...