AlgebraLab

Algebra I Recipe: Solving Systems of Linear Equations by Graphing

By G Redden

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).

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 300perdayinPhoenixand300 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

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