Question

Directions: For the following systems, determine whether or not the ordered triple (1, -1, -2) is a solution to the equations below.

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

Put the coordinate and check each

#1

`\\ \rm\Rrightarrow 3x-3y-z=2`

`\\ \rm\Rrightarrow 3(1)-3(-1)-(-2)=2`

`\\ \rm\Rrightarrow 3+3+2=2`

`\\ \rm\Rrightarrow 6+2=2`

`\\ \rm\Rrightarrow 8\\eq 2`

No

#2

`\\ \rm\Rrightarrow 2(1)-3(-1)-2=-3`

`\\ \rm\Rrightarrow 2+3-2=-3`

`\\ \rm\Rrightarrow 3\\eq-3`

Unless you did typing mistake on right hand side it's

• No

#3

`\\ \rm\Rrightarrow 1-1-2=-2`

`\\ \rm\Rrightarrow -2=-2`

Yes

#4

`\\ \rm\Rrightarrow 1+2(-1)-(-2)=0`

`\\ \rm\Rrightarrow 1-2+2=0`

`\\ \rm\Rrightarrow 1\\eq0`

No

#5

`\\ \rm\Rrightarrow 5(1)+1-5(-2)=16`

`\\ \rm\Rrightarrow5+1+10=16`

`\\ \rm\Rrightarrow 16=16`

Yes

#6

`\\ \rm\Rrightarrow 4(1)+5(-1)-6(-2)=-13`

`\\ \rm\Rrightarrow 4-5+12=-13`

`\\ \rm\Rrightarrow -1+12=-13`

`\\ \rm\Rrightarrow 11\\eq -13`

No