Question

find values of A and B such that the graph of the given equation will contain the given points. Ax+By = 3; (8,3), (13,7)

Answer 1

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:

• 8A + 3B = 3
• 13A + 7B = 3

By solving this system, we can find the values of A and B that satisfy both equations.

Step-by-step solution:

1. Multiply equation (1) by 7 and equation (2) by 3 to eliminate B:
2. 56A + 21B = 21 (Equation 3)
3. 39A + 21B = 9 (Equation 4)
4. Subtract equation (4) from equation (3) to find A:
5. 17A = 12
6. A = 12/17
7. Substitute A = 12/17 into either equation (1) or (2) to find B:
8. Using equation (1):
9. 8(12/17) + 3B = 3
10. 96/17 + 3B = 3
11. 3B = 3 - 96/17
12. 3B = 51/17 - 96/17
13. 3B = -45/17
14. B = -15/17

Therefore, the values for A and B are A = 12/17 and B = -15/17.