# Solve using elimination?

x-3y+4z=-4
4x+y-z=-11
3x+4y-6z=-9

Elimination method :

The system of equations are x - 3y + 4z = - 4 → ( 1 )

4x + y - z = - 11   → ( 2 )

3x + 4y - 6z = - 9 → ( 3 )

Solve equations (1) and (2) to eliminate the y - variables.

Multiply equation ( 2 ) by 3, then write the equations in column form, then add them.

x - 3y + 4z = - 4

12x + 3y - 3z = - 33

( + )____________________

13x + z = - 37 → ( 4 )

Solve equations (2) and (3) to eliminate the y - variables.

Multiply equation ( 2 ) by 4, then write the equations in column form, then subtract them.

16x + 4y - 4z = - 44
3x + 4y - 6z = - 9

( - )___________________

13x + 2z = - 35 → ( 5 )

Solve equations (4) and (5) to eliminate the x variable.

Write the equations in colmn form, then subtract them each other.

13x + z = - 37

13x + 2z = - 35

( - )_____________

- z = - 2

z = 2.

Substitute the value z = 2 in either of equations (4) or (5), for x.

Equation (  4) : 13x + z = - 37.

13x + 2 = - 37

13x = - 37 - 2 = - 39

x = - 39/13 = - 3.

Substitute the values x = - 3 and z = 2 in either of equations (1) or (2) or (3), for y.

Equation ( 1 ) : x - 3y + 4z = - 4.

- 3 - 3y + (4*2) = - 4

- 3y = - 4 + 3 - 8 = - 9

y = - 9/- 3 = 3.

The solution of the given system is (x, y, z) = (- 3, 3, 2).