1. Solving Systems of Equations by Graphing
Practice test 1 – Sept 8
LT # 1 – Sept 10

2. Recall:
SLOPE-INTERCEPT FORM
y = mx + b
slope
y-intercept
x + 2y = 6

3. Convert to slope-intercept form.
x + 2y = 6
2y = -x + 6
y = -1/2 x + 3

4. Y = -1/2 x + 3

5. . (1,5) y = 2x + 3 2) Obtain a second point using the slope, m.
1) Plot the point (0,3).
2) Obtain a second point using the slope, m.
(for every 2 rise, 1 run)
3) Draw a line through the two points.
y-intercept
slope
. (1,5)
(0,3) 
Write m as a fraction, and use rise over run, starting at the point containing the y-intercept, to plot this point. We express the slope, 2, as a fraction.

6. is a System of Linear Equations in two variables (x and y)
The solution to the system is the ordered pair (1, 2) because it satisfies both equations.

7. Simultaneous Linear Equations or System of Linear Equations
is a collection of linear equations with the same set of unknowns
They are solved by finding values that work for both variables (x and y) at the same time (simultaneously).

8. Solution of a System of Equations
A solution of a system of linear equations in two variables is an ordered pair (x, y) that makes BOTH equations true.
A system of equations can have 0, 1, or an infinite number of solutions.

9. x + y = 3 y = 3x + 3 (0, 3) x + y = 1 2y = -2x + 2 (2, -1) x + y = 8
Tell whether the ordered pair is a solution of the system of equations. Justify your answer.
x + y = 3
y = 3x + 3
(0, 3)
x + y = 1
2y = -2x + 2
(2, -1)
x + y = 8
x – 7 + y = 0
(4, 4)

10. Intersecting Lines
1 Solution: (3, -1)

11. Parallel Lines
No solution: { } or Ø

12. Infinitely many solutions:
Conciding Lines
Infinitely many solutions:
{(x, y)| x + y = 2}
READ AS: The set of all ordered pairs (x, y) such that “x + y = 2”.

13. GRAPH
SLOPE
Y-INTERCEPT
Intersecting
Different
Same or Different
Coinciding
Same
Parallel

14. Solutions of a System of
Linear Equations
Consistent
At least 1 solution
Inconsistent
No solution
Dependent
Infinite solutions
Independent
Unique/1 solution

15. EXISTENCE OF SOLUTION Number OF SOLUTIONS SLOPE Y-INTERCEPT
Consistent
Independent
(One - Point of Intersection)
Different
Same or Different
Dependent (Infinite - All points that lie on the line)
Same
Inconsistent
No solution

16. Solving Systems of Linear Equations Using Graphical Method
To find the solution of a system of linear equations graphically, determine the coordinates of the point of intersection of both graphs.

17. The Number of Solutions to a System of Two Linear Equations
Existence of Solution
Number of Solutions
Graph
Consistent and independent
Exactly one ordered-pair solution
Inconsistent
No solution
Consistent and dependent
Infinitely Many Solutions

18. Work in Pairs Without graphing, determine the ff:
a) existence of solution (consistent/inconsistent)
b) number of solutions (dependent/independent)
c) graph of the system (intersecting, parallel, coinciding)

19. 2) 3x + y = x – y = 3

20. 4) 4x + y = 2 4x + y = -3

21. 6) 3x – 2y = x + 3y = 9

22. 8) 3x + 2y = x + y = 2

23. 10) 2x + 5y = x – 2y = 9

24. 12) 3x – 4y = x – y = 16

25. - Review all files uploaded in Edmodo - Study Examples 1 & 2 NSM Bk2 p
- Review all files uploaded in Edmodo - Study Examples 1 & 2 NSM Bk2 p Review Questions # 5, 6, and 7 page 258

26. Online Self-Assessment