Answer:
A = 3, B = 4
Explanation:
To find A and B, we need to use the fact that the solution to the system of equations is (2,-4).
Substituting x=2 and y=-4 into the first equation, we get:
A(2) + 2(-4) = -2
Simplifying this equation, we get:
2A - 8 = -2
Adding 8 to both sides, we get:
2A = 6
Dividing both sides by 2, we get:
A = 3
So, we have found that A is equal to 3.
Now, substituting x=2 and y=-4 into the second equation, we get:
5(2) - B(-4) = 26
Simplifying this equation, we get:
10 + 4B = 26
Subtracting 10 from both sides, we get:
4B = 16
Dividing both sides by 4, we get:
B = 4
So, we have found that B is equal to 4.
Therefore, the values of A and B that satisfy the system of equations are A=3 and B=4.