2/3x - 1/4y + 5/8z = 0, 1/5x + 2/3y - 1/4z = -7 and -3/5x + 4/3y - 7/8z = -5

Question

2/3x - 1/4y + 5/8z = 0, 1/5x + 2/3y - 1/4z = -7, -3/5x + 4/3y - 7/8z = -5

solve for x,y,z.

 

Answer 1

Elimination method :

The system of equations are

         → ( 1 )

      → ( 2 )

  → ( 3 )

Change the equations from fraction form to linear equation.

The L.C.M of 3,4, and 8 in eq (1) is 24, so multiply eq (1) by 24.

                    → ( 4 )

The L.C.M of 5,3, and 4 in eq (2) is 60, so multiply eq (2) by 60.

         → ( 5 )

The L.C.M of 5,3, and 8 in eq (3) is 120, so multiply eq (3) by 120.

→ ( 6 )

Write the eqn's (4) & (5) in column form and add the equations to eliminate z - variable.

The resultant equation is → ( 7 )

To get the eq'ns (5) & (6) that contain opposite terms multiply the eq (5) by 7.

Write the equations in column form and subtract the equations to eliminate z - variable.

The resultant equation is → ( 8 )

Answer 2

To get the eq'ns (7) & (8) that contain opposite terms multiply the eq (7) by 13 and eq (8) by 14.

Write the equations in column form and subtract the equations to eliminate x - variable.

The resultant equation is .

Substitute the value of in eq (7), and solve for x.

Substitute the values of and in eq (4), and solve for z.

.

Therefore, solution of the given system is