Systems of Equations

Question

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

Answer 1

The equation is of a straight line.  The two points are (8,3) and (13,7).  The double point form of the straight line is (y-3)=[(7-3)/(13-8)](x-8) or y-3=[4/5](x-8) or y-3=4x/5-32/5 and so 4x/5-y=32/5-3 or 4x-5y=32-15=17

4x-5y=17 is the Ax+By=C form. 

Answer 2

given the two separate coordinates, one can write an equation corresponding to each coordinate.  A given equation would basically indicate that the coordinate satisfies (x,y) in the equation.

 

With two equation and two unknowns, we can solve for A and B (two ways are through substitution and elimination...one can also use matrices).