Determine whether or not the order triple (1,-1,-2) is the solution

Question

1. 3x-3y-z=2
2. 2x-3y+z=-3
3. x+y+z=-2
4. x+2y-z=0
5. 5x-y-5z=16
6. 4x+5y-6z=-13

Answer 1

(1, -1, -2), where x=1, y=-1, z=-2

1) 3x-3y-z=2

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

3+3+2=2

8=2 X

Not the solution, as the order triple does not make this equation true.

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

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

2+3-2=-3

3=-3 X

Not the solution, as the order triple does not make this equation true.

3) x+y+z=-2

1+(-1)-2=-2

-2=-2 Yes

This is the solution, as the order triple makes this equation true.

4) x+2y-z=0

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

1-2+2=0

1=0 X

Not the solution, as the order triple does not make this equation true.

5) 5x-y-5z=16

5(1)-(-1)-5(-2)=16

5+1+10=16

16=16 Yes

This is the solution, as the order triple makes this equation true.

6) 4x+5y-6z=-13

4(1)+5(-1)-6(-2)=-13

4-5+12=-13

-1+12=-13

11=-13 X

Not the solution, as the order triple does not make this equation true.

Answer 2

This is just a matter of plugging in the values to see if you get an equality. The ordered triple (1, -1, -2) means x = 1, y = -1, and z = -2 so plug them into each equation. The first one would give you:

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

3 - -3 - -2 = 2

3 + 3 + 2 = 2

8 = 2

and since 8 does not equal 2, (1, -1, -2) is NOT a solution to the equation 3x - 3y - z = 2

Now, repeat this for all the other equations.