Question

write two equations in one variable that have the same number of solutions as this equation solve 49x + 9 equals 49x + 83

Answer 1

$49x+9=49x+83$

To solve this equation you need to clear the variable x, as follow:

$\begin{gathered} 49x-49x=83-9 \\ 0=74 \end{gathered}$As 0 is not equal to 74. The equation has no solution.

To write two equations with no solutions you write equations that when you clear the variable the solution make no mathematical sense:

$\begin{gathered} y-45=y+9 \\ y-y=9+45 \\ 0=54 \end{gathered}$$\begin{gathered} -5z=25-5z \\ -5z+5z=25 \\ 0=25 \end{gathered}$