How do you solve the system #y = - 2/3x# and #2x + 3y = 5# by graphing?
There is no solution to this system of equations
You have two equations. What is normally meant by 'solve' is really the question: What are the value for
So the question now is: Why do they not cross?
This can be re-written as
Now compare this to
Notice that the coefficient in front of
This is the gradient. As the gradient (slope) is the same for both equations they are parallel.
This means that they NEVER cross. So they do NOT share the same values at any point.