Algebra I Recipe: Solving Systems of Linear Equations by Graphing
By G Redden
Graphing Method
- Solve both equations for y.
- Graph each equation using y = mx + b.
- 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).
1.
2x - 3y = 1 and x + y = 3
2.
3x - 2y = 6 and 6x - 4y = 12
3.
3x - 2y = 6 and 3x - 2y = 2
4.
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 |
||||||||
