What happens graphically when you set equations equal to each other?
I know you can solve the equations to find points where they meet, but how exactly does this work graphically?
I know you can solve the equations to find points where they meet, but how exactly does this work graphically?
1 Answer
To solve a system of equations graphically we look for the point of intersection.
Eg. Consider:
#y = x# and#y = 1-x#
graph{(y-x)(y+x-1)=0 [-2.5, 2.5, -1.25, 1.25]}
Using the graphs we would estimate that the point of intersection is
The above example is trivial as we can can both confirm the above solution a derive it algebraically.
If however we have more complex function, for example:
# y = lnx# and#y=2-x#
Then we cannot derive an algebraic solution:
graph{(y-lnx)(y+x-2)=0 [-2.5, 2.5, -1.25, 1.25]}
Here we estimate a solution