Final answer:
To find A and B in the given linear system of equations, we substitute the x and y values from the solution into each equation and solve for A and B separately.
Step-by-step explanation:
To find the values of A and B in the linear system of equations Ax + 4y = -10 and 3x - By = 22, we can use the given solution (2,-4) and substitute the x and y values accordingly.
Substituting x = 2 and y = -4 into the first equation, we get A(2) + 4(-4) = -10. Simplifying this equation, we have 2A - 16 = -10. Adding 16 to both sides, we get 2A = 6. Dividing both sides by 2, we find that A = 3.
Substituting x = 2 and y = -4 into the second equation, we get 3(2) - B(-4) = 22. Simplifying this equation, we have 6 + 4B = 22. Subtracting 6 from both sides, we get 4B = 16. Dividing both sides by 4, we find that B = 4.