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

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

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

$\\ \rm\Rrightarrow 3+3+2=2$

$\\ \rm\Rrightarrow 6+2=2$

$\\ \rm\Rrightarrow 8\neq 2$

No

#2

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

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

$\\ \rm\Rrightarrow 3\neq-3$

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

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

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

$\\ \rm\Rrightarrow 1\neq0$

No

#5

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

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

$\\ \rm\Rrightarrow 16=16$

Yes

#6

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

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

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

$\\ \rm\Rrightarrow 11\neq -13$

No