Final answer:
To find the values of A and B, we use the given points (8,3) and (13,7) to create a system of equations based on the equation Ax + By = 3. Solving this system, we find that A = 12/17 and B = -15/17.
Step-by-step explanation:
To find the values of A and B such that the equation Ax + By = 3 contains the given points (8,3) and (13,7), we can set up two separate equations using these points and solve for A and B.
Using the first point (8,3), we substitute x with 8 and y with 3:
8A + 3B = 3
(1)
Using the second point (13,7), we substitute x with 13 and y with 7:
13A + 7B = 3
(2)
We now have a system of two linear equations:
By solving this system, we can find the values of A and B that satisfy both equations.
Step-by-step solution:
- Multiply equation (1) by 7 and equation (2) by 3 to eliminate B:
- 56A + 21B = 21 (Equation 3)
- 39A + 21B = 9 (Equation 4)
- Subtract equation (4) from equation (3) to find A:
- 17A = 12
- A = 12/17
- Substitute A = 12/17 into either equation (1) or (2) to find B:
- Using equation (1):
- 8(12/17) + 3B = 3
- 96/17 + 3B = 3
- 3B = 3 - 96/17
- 3B = 51/17 - 96/17
- 3B = -45/17
- B = -15/17
Therefore, the values for A and B are A = 12/17 and B = -15/17.