Question

Find the ordered triple of these equations.

 x + 2y + 2z = 0

2x + y + z = 3

x - 3y - z = 1

Be sure to put coordinates in parentheses.

Answer 1

Elimination method

Given equations are x+2y+2z = 0 ----> (1)

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

x-3y-z = 1 ----->(3)

To eliminate x value subtract equation (1) from (3).

x - 3y- z = 1

x+2y+2z = 0

(-)(-) )(-)

____________

-5y-3z = 1 --------> (4)

Multipl to each side of equation (1) by 2.

2x+4y+4z = 0 ------>(5)

To eliminate the x value subtract the equation (2) from (5).

2x+4y+4z = 0

2x+ y +z    = 3

(-) (-)  (-)   (-)

___________

3y+3z = -3 -------> (6)

To eliminate the z value add the equations (4) and (6).

-5y-3z = 1

3y+3z = -3

__________

-2y = -2

Divide to each side by negitive 2.

-2y/-2 = -2/-2

y = 1

Substitute the y value in (6).

3(1)+3z = -3

3z = -6

Divide to each side by 3.

3z/3 = -6/3

z = -2

Substitute the y,z values in (1).

x+2(1)+2(-2) = 0

x+2-4 = 0

x-2 = 0

Add 2 to each side.

x-2+2 = 0+2

x = 2

Check

substitute the values in equation (1), (2),(3).

x+2y+2z = 0

2+2(1)+2(-2) = 0

0 = 0

2x+y+z = 3

2(2)+1-2 = 3

3 = 3

x-3y-z = 1

2-3(1)-(-2) = 1

1 = 1

Orderd triple of given equations  is x = 2, y = 1,z = -2