The point of intersection of the graphs of the equations of the system

Question

Ax – 4y = 9
4x + By = –1
is (–1, –3). Explain how to find the values of A and B, then find these values.

Answer 1

The point (-1,-3) must lie on both curves. Thus
-A -4*(-3) = 9
-A +12 = 9
A = 3
and
4*(-1) +B*(-3) = -1
Solve that for B

Answer 2

x = - 1

y = - 3

A x – 4 y = 9

A * ( - 1 ) - 4 * ( - 3 ) = 9

- A + 12 = 9

- A = 9 - 12

- A = -3 Multiply both sides by - 1

A = 3

4 x + B y = –1

4 * ( - 1 ) + B * ( - 3 ) = - 1

- 4 - 3 B = - 1

- 3 B = - 1 + 4

- 3 B = 3 Divide both sides by - 3

B = 3 / - 3

B = - 1