Question

if a b and c are three different numbers which of the following equations has infinitely many solutions

a. ax=bx+c
b. ax+b=ax+c
c. ax+b=ax+b

Answer 1

Answer:

c. ax+b=ax+b

Step-by-step explanation:

To know what equation has infinite solutions, you first try to simplify the equations:

a.

$ax=bx+c\\\\(a-b)x=c\\\\x=\frac{c}{a-b}$

In this case you have that a must be different of b, but there is no restriction to the value of c, then c can be equal to a or b.

b.

$ax+b=ax+c\\\\b=c$

Here you obtain that b = c. But the statement of the question says that a, b and c are three different numbers.

c.

$ax+b=ax+b\\\\0=0$

In this case you have that whichever values of a, b and are available solutions of the equation. Furthermore, when you obtain 0=0, there are infinite solutions to the equation.

Then, the answer is:

c. ax+b=ax+b