Question

4 which of the systems of equations has a solution of (-2,6)? a \

$$\begin{cases} y - 2x = 2 \\\\ y + 2x = 10 \\end{cases}$$

b \

$$\begin{cases} x - y = 9 \\\\ y = x + 9 \\end{cases}$$

c \

$$\begin{cases} y = 2x + 10 \\\\ y = 3x - 6 \\end{cases}$$

d \

$$\begin{cases} x + 2y = 10 \\\\ -4x - y = 2 \\end{cases}$$

Explanation:

Step1: Test point (-2,6) in A

Substitute $x=-2, y=6$ into system A:
First equation: $6 - 2(-2) = 6 + 4 = 10
eq 2$
Second equation: $6 + 2(-2) = 6 - 4 = 2
eq 10$

Step2: Test point (-2,6) in B

Substitute $x=-2, y=6$ into system B:
First equation: $-2 - 6 = -8
eq 9$
Second equation: $6 = -2 + 9 = 7
eq 6$

Step3: Test point (-2,6) in C

Substitute $x=-2, y=6$ into system C:
First equation: $6 = 2(-2) + 10 = -4 + 10 = 6$
Second equation: $6 = 3(-2) - 6 = -6 - 6 = -12
eq 6$

Step4: Test point (-2,6) in D

Substitute $x=-2, y=6$ into system D:
First equation: $-2 + 2(6) = -2 + 12 = 10$
Second equation: $-4(-2) - 6 = 8 - 6 = 2$

Answer:

D.

$$\begin{cases} x + 2y = 10 \\ -4x - y = 2 \end{cases}$$