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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).
ExamplesExamples:
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 = 7
300x + 675y = 2850




G Redden

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