Question

Consider the equation c= ax-bx, where a,b, and c are whole numbers. Which of the following result in values of a, b, and c so that the original equation has exactly one solution? Justify your answers.

1.) a-b=1, c=0
2.) a=b, c≠0
3.) a=b, c=0
4.) a≠b, c=0

Answer 1

$\\ \sf\longmapsto c=ax-bx$

• Take x common

$\\ \sf\longmapsto c=x(a-b)$

• If a-b=1 then c=-x(infinite solutions)

If a=b

$\\ \sf\longmapsto c=0$

Option C is the correct ans