Which values for A and B will create infinitely many solutions for this system of equations?

Ax-y=8

2x+y=B

A = 2. B - 8

A=-2. B=8

A = 2. B=-8

A--2.8--8

see explanation below

Step-by-step explanation:

Let's write again the system:

Ax - y = 8

2x + y = B

Now we want to know which values for A and B will turn the system with infinite solutions. To know this, we need to apply the following. A system of equation has the following general expression:

ax + by = e

cx + dy = f

To know if a system has infinite solutions, we have to acomplish the following:

a * d = b * c and b * f = d * e

so, let's replace the options into these expression, and the ones who match this, would be the values of A and B:

1. A = 2 and B = - 8

2x - y = 8

2x + y = - 8

a * d = b * c

a * d = 2 * 1 = 2

b * c = - 1 * 2 = - 2

These are not the same, so we can discart this option.

2. A = - 2 B = 8

-2x - y = 8

2x + y = 8

a * d = b * c

a * d = - 2 * 1 = - 2

b * c = - 1 * 2 = - 2

This match, let's see the other

b * f = d * e

b * f = (-1) * (-8) = 8

d * e = 1 * 8 = 8

This option perfectly match, so this is the correct option. A = - 2 and B = 8