solve:ax+by=c?

Answer 1

This is a straight line. It can be rewritten:

by = -ax + c

y = (-a/b)x + (c/b)

(-a/b) is the slope of the line (how much y increases every time x inceases by 1).
c/b is the "intercept", the point where the line crosses the y axis (i.e., the y value when x=0)

---

Of course, if b=0 then we are in trouble because we divide by 0.

Instead we would write:

ax + 0 y =c
ax = c
x = c/a (on a x-y graph, this would be a vertical line going through x = c/a)

If a = 0 AND b = 0, then c = 0 and it is not even a line.

Answer 2

For a=0 and b=0 and c different from 0 there are no solutions.
e.g
0x+0y=c
0=c but c is not equal to 0, therefore no matter what you put for x and y the equation will always be false.

For a=0 the solution is y=c/b . For b=0 the solution is x=c/a. For x and y different from 0 there is infinite number of solutions.
e.g
ax+by=c and a,b,c are not equal to 0 then
by=-ax+c
y=(-ax+c)/b
solution is a sae of pair of numbers for which the above equation is true (infinite number of solutions)

If a and b and c are equal to 0 then there is infinite number of solutions.
e.g
0x+0b=0 which is equal to 0+0=0 which is 0=0. as you see, whatever value you put for x and y the equation will always be true.

Answer 3

C=ax+by

Answer 4

Ax + By = C has no solution or an infinite number of solutions.

http://www.analyzemath.com/line/line.htm or searching google might help.