Answer:
Options B and E.
Explanation:
We want to see for which systems the point (-3, 2) is a solution (a solution of a system means that both equations intersect in that point).
The point (-3, 2) is a solution of the system only if this point belongs to both linear equations in the system.
Then for each system, we need to replace x by -3 and y by 2 in both equations and see if the equality is true or not.
A)
6x - y = 15
-3x + 4y = -18
In the first equation we have:
6*(-3) - (2) = 15
-18 - 2 = 15
-20 = 15
This is false, so we can discard option A.
B)
2x + y = -4
3x + 2y = -5
In the first equation we have:
2*(-3) + 2 = -4
-6 + 2 = -4
-4 = - 4
This is true, now let's look at the other equation.
3*(-3) + 2*(2) = -5
-9 + 4 = -5
-5 = - 5
This is also true, then the point (-3, 2) is a solution for both equations, then the point (-3, 2) is a solution for the system.
C)
x + 8y = 19
4x - 5y = 2
In the first equation we have:
(-3) + 8*(2) = 19
-3 + 16 = 19
13 = 19
This is false, then we can discard option C.
D)
8x + y = 22
-2x - 5y=4
In the first option we have:
8*(-3) + 2 = 22
-24 + 2 = 22
-22 = 22
This is false, so we can discard option D.
E)
5x - y = -17
x + 4y = 5
In the first option we have:
5*(-3) - (2) = -17
-15 - 2 = -17
-17 = -17
This is true, now let's look at the other equation:
(-3) + 4*(2) = 5
-3 + 8 = 5
5 = 5
This is also true, then the point (-3, 2) is a solution for both equations in the system, which means that the point (-3, 2) is a solution for the system.
Then the correct options are B and E.