Question

select the correct answer.
which system of equations has a solution of (1, 2, 3)?

a. -2x - 2z = -8
y + 3z = 7
x + y - 3z = -3

b. x + y + 2z = 9
2x + 2y + 3z = 15
x - z = -2

c. x + y = 3
y - z = 1
x + y - z = 0

d. -3x + 2y + z = 4
x - y + 2z = 5
x - y - z = -2

Explanation:

Step1: Test (1,2,3) in Option A

Substitute $x=1$, $y=2$, $z=3$:

1. $-2(1) - 2(3) = -2 - 6 = -8$ ✔️
2. $2 + 3(3) = 2 + 9 = 11

eq 7$ ❌

Step2: Test (1,2,3) in Option B

Substitute $x=1$, $y=2$, $z=3$:

1. $1 + 2 + 2(3) = 1 + 2 + 6 = 9$ ✔️
2. $2(1) + 2(2) + 3(3) = 2 + 4 + 9 = 15$ ✔️
3. $1 - 3 = -2$ ✔️

Step3: Verify no need for further tests

All equations in B are satisfied, so we can stop here.

Answer:

B. $x + y + 2z = 9$; $2x + 2y + 3z = 15$; $x - z = -2$