Question

solve 49x+9=49x+83a. does the equation have one solution, no solution, or infinity many solutions B.write two equations in one variable that the same number of solutions as this equation

Answer 1

a) We have the equation:

`49x+9=49x+83`

We can try to solve this as:

`\begin{gathered} 49x+9=49x+83 \\ 49x-49x+9=83 \\ (49-49)x+9=83 \\ 9=83\longrightarrow\text{Not true} \end{gathered}`

This equation does not have a solution, as there is no value of x for which 9 = 83.

b) We have to write two equations in one variable that have the same number of solutions as the previous equation (in this case, no solution).

The condition for this system of linear equations is that the coefficients of x are the same while the independent term have to be different.

An example of this is:

`x+1=x+2`

There is no value of x that can make this equation became true. This means that it has no solution.

Answer:

a) No solution

b) x+1 = x+2