1. Solve Systems of Equations By Graphing

2. VOCABULARY
A system of two linear equations, also called a linear system, in two variables x and y consists of two equations that can be written in the following form:
Ax + By = C
Dx + Ey = F

3. VOCABULARY
A solution of a system of linear equations in two variables is an ordered pair (x, y) that satisfies both equations.
At least 1 solution: CONSISTENT
No solutions: INCONSISTENT [graph is parallel lines]
Exactly 1 solution: INDEPENDENT
Infinitely many solutions: DEPENDENT

4. VOCABULARY
CONSISTENT INDEPENDENT
CONSISTENT DEPENDENT
INCONSISTENT

5. EXAMPLES
1) Check whether the ordered pair is a solution of the systems.
(7, 4) y + x = 11
y – 2x = -10

6. EXAMPLES
1) Check whether the ordered pair is a solution of the systems.
(1, 5) 3x - 2y = 7
y = 2x + 1

7. EXAMPLES
2) Graph the linear system and estimate the solution. Then check the solution algebraically.
y = –3x + 5
y = 2x – 5

8. EXAMPLES
2) Graph the linear system and estimate the solution. Then check the solution algebraically.
3x + y = 7
y = 2x - 3

9. EXAMPLES
3) Graph the linear systems. Then classify as consistent & independent, consistent & dependent, or inconsistent.
4x + 3y = 9
-2x +3y = -6

10. EXAMPLES
3) Graph the linear systems. Then classify as consistent & independent, consistent & dependent, or inconsistent.
-x + y = 3
y = x - 7