Question

select the correct answer.
which system of equations has a solution of (1, 3, -1)?
a. $x + y = 4$
$y - z = 2$
$x + y - z = -1$
b. $3x - y = 8$
$2y - z = 5$
$x - y + z = -1$
c. $-2x + 2y = 4$
$y + 7z = -4$
$x - y - z = 4$
d. $x + 2y = 7$
$y + 2z = 1$
$x - y - z = -1$

Explanation:

Step1: Substitute $x=1,y=3,z=-1$ into Option A

Check each equation:

1. $1+3=4$ ✔️
2. $3-(-1)=4

eq2$ ❌

Step2: Substitute $x=1,y=3,z=-1$ into Option B

Check each equation:

1. $3(1)-3=0

eq8$ ❌

Step3: Substitute $x=1,y=3,z=-1$ into Option C

Check each equation:

1. $-2(1)+2(3)=-2+6=4$ ✔️
2. $3+7(-1)=3-7=-4$ ✔️
3. $1-3-(-1)=1-3+1=-1

eq4$ ❌

Step4: Substitute $x=1,y=3,z=-1$ into Option D

Check each equation:

1. $1+2(3)=1+6=7$ ✔️
2. $3+2(-1)=3-2=1$ ✔️
3. $1-3-(-1)=1-3+1=-1$ ✔️

Answer:

D.

$$\begin{aligned} x + 2y &= 7 \\ y + 2z &= 1 \\ x - y - z &= -1 \end{aligned}$$