1. Solving Systems of Equations
Graphing/substitution Method

2. PART I. GUIDED NOTES: A system of linear equations is a set of two or more equations with the same variable. The solution of a system in x and y is any ordered pair (x, y) that satisfies each of the equations in the system. The solution of a system of equations is the intersection of the graphs of the equations.

3. Part I. Guided Notes Cont.
NO SOLUTION
The lines intersect so there is one solution.
y – 2x = 7
Y = 2x + 3
The lines are parallel so there are no solutions.
x + 2y = 7
x = y + 4
The lines are the same so there are infinitely many solutions.
ONE SOLUTION
-3x = 5 – y
2y = 6x + 10
INFINITE SOLUTION

4. Profit
Loss
In business, the point at which income equals expenses is called the break-even point. When starting a business, people want to know the point a which their income equals their expenses, that’s the point where they start to make a profit. In the example above the values of y on the blue line represent dollars made and the value of y on the dotted red line represent dollars spent.

5. To review systems (tortoise vs rabbit)

6. PART II. Question(s): Tyler leaves the trailhead at dawn to hike 12 miles toward the lake, where his friend Phil is camping. At the same time, Phil starts his hike toward the trailhead. Tyler is walking uphill so he averages only 1.5 mi/hr, while Phil averages 2.5 mi/hr walking downhill. When and where will they meet?

7. Tyler starts at the trailhead so he increases his distance from it as he hikes 1.5 mi/hr for x hours. Phil starts 12 miles from the trailhead and reduces his distance from it as he hikes 2.5 mi/hr for x hours.

8. .The table shows the x-value that gives equal y-values for both equations. When x = 3, both y-values are So the solution is the ordered pair (3, 4.5). We say these values “satisfy” both equations.

9. What do you notice about y when x increases in each equation
What do you notice about y when x increases in each equation? Why are the values different?

10. On the graph this solution is the point where the two lines intersect..

11. Use the graphing calculator https://www. desmos
Use the graphing calculator to solve each system of equations. Determine if the solution is 1, none or infinite.

14. Additional Practice (optional)

15. Solving Systems with Substitution (see example 1 and 2)

16. Visit the Site and Practice:

17. Games:
(graphing linear equations)
(millionaire equation game)