1. Algebra 1
Section 7.1

2. Definition
A system of linear equations is made up of two or more linear equations.
Any ordered pair that makes all of the equations true is a solution to the system of equations.

3. Is (11, 2) a solution to the system?
Example 1
x – y = x + y = 9
Is (11, 2) a solution to the system?
11 – 2 = (11) + 2 = 9
True False
(11, 2) is not a solution.

4. Example 1 x – y = 9 2x + y = 9 6 – (-3) = 9 2(6) + (-3) = 9 True True
Is (6, -3) a solution to the system?
6 – (-3) = (6) + (-3) = 9
True True
(6, -3) is a solution.
In fact, it is the only solution.

5. Solving a System by Graphing
Graph both equations on the same coordinate plane.
Identify the solution, the coordinates of the point of intersection.

6. Solving a System by Graphing
Check the solution by substituting it into each equation.

7. Example 2 Solve the system by graphing. y = -x – 2 m = -1
y-int.: (0, -2)
y = x – 4
m = 1
y-int.: (0, -4)

8. Example 2 y
y = -x – 2
y = x – 4 x
Solution: (1, -3)
(1, -3)

9. Example 3 Solve the system by graphing. x – y = -5 y = x + 5 m = 1
y-int.: (0, 5)
3x + y = -7
y = -3x – 7
m = -3
y-int.: (0, -7)

10. Example 3 y
x – y = -5
(-3, 2)
3x + y = -7 x
Solution: (-3, 2)

11. Solving a System by Graphing
Sometimes a system of equations contains equations that name parallel lines.
Since parallel lines have no points in common, such a system of equations has no solution.

12. Solving a System by Graphing
Sometimes a system of equations contains graphs that are the same line.
These are said to coincide.
The solution is the set of all the points on the line.

13. Example 4a Both equations have the same slopes and y-intercepts.
Their graphs coincide.
Solution: y = -x + 3

14. Example 4b
The equations have the same slope but different y-intercepts.
Their graphs are parallel.
Solution: Ø

15. Possible Solutions to a System
Intersecting Lines
Graph
Number of Solutions
Answer
one solution
ordered pair

16. Possible Solutions to a System
Parallel Lines
Graph
Number of Solutions
Answer
no solution Ø

17. Possible Solutions to a System
Coinciding Lines
Graph
Number of Solutions
Answer
infinite solutions
all the points on the line

18. Example 5
Both functions will need to be graphed on the same coordinate plane.
a(x) = 250x
b(x) = 350x

19. Example 5 For both options, Drew will have spent $5500 at 10 mo.
Note that loan B will pay the car off at a faster rate as long as the price of the car is more than $5500.

20. Homework: pp