Question

* WORTH 30 Points *

Jeremy further remembers that the class looked at another system of equations with the same first equation (-2x+ 3y= 18), but he recalls that this other system of equations had no solution. Write an equation for Jeremy which, if paired with the first equation, would result in a system of equations with no solution. Show the steps you took to find your answer.

Answer 1

Any multiple of (-2x+3y=18) would constitute an "other equation" forming a system with an infiinite number of solutions. The reason for that is that the two equations would be "dependent."

On the other hand, looking at the system

-2x+ 3y= 18
-2x+ 3y= 19

we see that there is no solution. Why? Because -2x + 3y cannot equal 18 and 19 at the same time. You'd have two non-intersecting, parallel lines.