Find the ordered triple of these equations 2x+5y-3z=-5, 3x+2y+7z=15, 5x-4y+6z=34

Question

Im not sure how to solve this type of system. Can someone please explain how its supossed to be solved.

Answer 1

The system of equations are

2x + 5y - 3z = - 5 → ( 1 )

3x + 2y + 7z = 15 → ( 2 )

5x - 4y + 6z = 34  → ( 3 )

To get the eq'ns (1) & (2) that contain opposite terms multiply the eq (1) by - 3, and multiply the eq (2) by 2.

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

The resultant equation is - 11y + 23z = 45 → ( 4 )

To get the eq'ns (2) & (3) that contain opposite terms multiply the eq (2) by - 5, and multiply the eq (3) by 3.

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

The resultant equation is - 22y - 17z = 27  → ( 5 )

To get the eq'ns (4) & (5) that contain opposite terms multiply the eq (4) by 2.

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

The resultant equation is 63z = 63 ⇒ z = 63/63 = 1.

Substitute the value of z = 1 in eq (4), and solve for y.

- 11y + 23z = 45

- 11y + 23(1) = 45

- 11y = 45 - 23 = 22

⇒ y = 22/- 11 = - 2.

Substitute the value of y = - 2 and z = 1 in eq (1), and solve for x.

2x + 5y - 3z = - 5

2x + 5(- 2) - 3(1) = - 5

2x - 10 - 3 = - 5

2x = - 5 + 13 = 8

⇒ x = 8/2 = 4.

Therefore, ordered tripple of the given system is (x, y, z ) = (4, - 2, 1).