Question

Two solutions of the equation Ax+By = 1 are (2, -1) and (-3,-2). Find A and B.

Answer 1

Substitute in the values of both given coordinates & form 2 equations:

`\left \{ {{A(2)+B(-1)=1} \atop {A(-3)+B(-2)=1}} \right. \\\\=\left \{ {{2A-B=1} \atop {-3A-2B=1}} \right.`

Find the value of B from the equation 2A - B = 1:

`2A-B=1\\-B=1-2A\\B=2A-1`

Substitute in the B-value to the other equation:

`-3A-2B=1\\-3A-2(2A-1)=1\\-3A-4A+2=1\\-7A=1-2\\-7A=-1\\A=(-1)/(-7) =(1)/(7)`

Find the B-value using the equation from before:

`B=2A-1=2((1)/(7))-1=(2)/(7) -(7)/(7) =-(5)/(7)`

Therefore the equation Ax + By = 1 would equal:

`(1)/(7) x-(5)/(7) y=1`