Find A and B if the graph of Ax + By = 12 passes through (2, 1) and is parallel to the graph of 2x − 7y = 3.

A is -8

B is 28

Step-by-step explanation:

Let us rewrite the equation in the standard format of y = mx + b

By = -Ax + 12

y = (-A/B)x + 12/B

Now, since the line is parallel to the line given below, then their slopes must be equal

2x - 7y = 3

7y = 2x - 3

y = (2/7)x - 3/7

slope here is 2/7

Thus;

-A/B = 2/7

let’s now insert the point that the line passes through

We have;

1 = (-A/B)2 + 12/B

but -A/B = 2/7

1 = 4/7 + 12/B

12/B = 1 - 4/7

12/B = 3/7

B = (7 * 12)/3

B = 28

-A/28 = 2/7

-7A = 56

A = 56/-7

A = -8

the answer is n