Algebra I Recipe: Solving Systems of Linear Equations by Graphing
Graphing Method
1. Solve both equations for y.
2. Graph each equation using y = mx + b.
3. Determine the solution by the graph.
• If the two lines intersect, the solution is the point where the two lines intersect.
• If the two lines are parallel, the solution is NO SOLUTION.
• If the two lines overlap, the solution is infinitely many solutions (IMS).
Examples:
 2x - 3y = 1 and x + y = 3
 3x - 2y = 6 and 6x - 4y = 12
 3x - 2y = 6 and 3x - 2y = 2
Real Life: Your family is planning a 7 day trip to Arizona. You estimate that it will cost \$300 per day in Phoenix and \$675 per day in the Grand Canyon. Your total budget for the 7 days is \$2850. How many days should you spend in each location?

 time spent in Phoenix + time spent in the Grand Canyon = total vacation time

 daily rate in Phoenix * time spent in the Grand Canyon + daily rate in Phoenix * time spent in the Grand Canyon = total 7 day budget HINT: Translate the problem into relationships and variables. In this case, let x represent the number of days spent in Phoenix and y represent the number of days spent in the Grand Canyon. x + y = 7300x + 675y = 2850

G Redden

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