Emma substitutes 3 for x in a one-variable linear equation and finds that it makes the equation true. She then substitutes 5 for x in the same linear equation and finds out that 5 also makes the equation true. What can you conclude about the number of solutions of the equation? Explain your reasoning.

Guest Apr 29, 2017

#1**+1 **

If x can take more than one value, then you may have many, many or perhaps an infinite number of solutions.

Guest Apr 29, 2017

#2**+1 **

Emma substitutes 3 for x in a one-variable linear equation and finds that it makes the equation true. She then substitutes 5 for x in the same linear equation and finds out that 5 also makes the equation true. What can you conclude about the number of solutions of the equation? Explain your reasoning.

**I think you are correct guest but you have not tried to give a reason.**

What about if the equation was

(x-3)(x-5)=0 x=3 and x=5 both make it true..

Oh that is no good because f(x)=(x-3)(x+5) is not linear.

I think the eqation is

mx+b=k

but m,b and k are all constants.

If this is true for x=5 and x=3 then m must equal 0 and k must equal b

So this must be the formula for a horizonal line.

f(x)=k

so any value of x will satisfy it. There are an infinite number of solutions :)

Melody
Apr 30, 2017