We want to find the values of A and B such that the given system of equations has no solutions. We will find that the values of A and B can be:
B = -4.5
A = 6
When a system of equations has no solutions?
A system of linear equations has no solutions when the lines are parallel (so the lines never do intercept).
Here the system is:
3x + 4y = A
Bx – 6y = 15
Remember that two lines are parallel if and only if they have the same slope and different y-intercept, then let's write both equations in the slope-intercept form:
y = A/4 - (3/4)*x
y = -15/6 + (B/6)*x
So we must have:
B/6 = -3/4
A/4 ≠ -15/6
From the first one we get:
B = (-3/4)*6 = -4.5
From the second one we get:
A ≠ (-15/6)*4 = -10
Then from the given pairs, the only one that causes the system to have no solutions is:
B = -4.5
A = 6
If you want to learn more about systems of equations, you can read:
https://brainly.com/question/13729904
