The graph of a system of equations shows the solution to be at (-6, 2). Which two of the following equations could
make up this system ? Make sure you choose both equations.
2x - 3y = -6
4x - y = 26
3x + 2y = -14
x-y = -2
x+y=-4

Step-by-step explanation:

The graph shows the solution (-6,2)

i.e at x= -6 y=2

Analysis of each of the answers, since we can't write the equation of a straight line with only that information i.e the single point

Then,

Option 1

1. 2x - 3y = -6

x= -6 y=2

Then let insert x=-6 and y =2

2(-6)-3(2)

-12-6

-18.

Since -18 ≠ -6, then this is not the equation of the line and doesn't make up the system

Option 2

2. 4x - y = 26

Inserting x=-6 and y=2

4(-6)-(2)

-24-2

-26

Since -26 ≠ 26, then this is not the equation of the line and doesn't make up the system

Option 3

3. 3x + 2y = -14

Inserting x=-6 and y=2

3(-6)+2(2)

-18+4

-14

Since -14 ≠ -14 then this is the equation of the line and it make up the system.

Option 4

x-y = -2

Inserting x=-6 and y=2

(-6)-(2)

-6-2

-8

Since -8≠ -2, then this is not the equation of the line and doesn't make up the system

Option 5

5. x+y=-4

Inserting x=-6 and y=2

(-6)+(2)

-6+2

-4

Since -4 ≠ -4, then this is the equation of the line and it makes up the system.

Then, there are two option that make up the system

3. 3x + 2y = -14

And

5. x+y=-4