The graphs of which of these pairs of linear equations intersect at the point (-3, 2)? Select all that apply.
A 6x - y = 15
-3x + 4y = -18
B. 2x + y = -4
3x + 2y = -5
C. X + 8y = 19
4x - 5y = 2
D. 8x + y = 22
-2x - 5y=4
E5x - y = -17
x + 4y = 5

Answer:

Options B and E.

Step-by-step 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.

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