Sometimeswe wish to look at pairsof equationsand examinewherethey havecommonsolutions.Consider
the linearand quadraticgraphsof the previousexamples.We can sketchthemon the sameaxes:
We can see that the graphsintersectat two points.It turnsout that we can solvethe problemof findingthe
pointsof intersectionsanalyticallyand also by usingour graphingcalculator. Let’s revieweachmethod.
AnalyticalSolution
Sincethe pointsof intersectionare on eachgraph,we can use substitution,settingthe general -coordinates
equalto eachother, and solvingfor
We substituteeachvalueof into one of the originalequationsand find the pointsof intersectionsat
and
GraphingCalculatorSolution
Oncewe haveenteredthe relationshipson theY=menu,we press2nd[CALC]and choose#5Intersection
fromthe menu.We thenare promptedwith a cursorby the calculatorto indicatewhichtwo graphs
we wantto workwith.Respondto the nextpromptby pressingthe left or rightarrowsto movethe
cursornear one of the pointsof intersectionand press[ENTER]. Repeatthesestepsto find the location
of the secondpoint.
We can use equationsand graphsto modelreal-lifesituations.Considerthe followingproblem.
Example6:LinearModeling