1. Solving Systems with 2 Variables U3.1

2. Vocabulary
A system of linear equations in two variables x and y, also called a linear system, consists of two or more equations that can be written in the following form.
Ax + By = C
Dx + Ey = F
A solution of a system of linear equations in two variables is an ordered pair (x,y) that satisfies each equation.

3. The solution is the point of intersection which is (6, -1).
Solve by Graphing
Example 1.
Solve by graphing
y = -x + 5
-2y = -3x + 20
y = 3/2 x -10
The solution is the point of intersection which is (6, -1).

4. Classifying Systems System with at least one solution:
is called Consistent.
Exactly one solution is consistent - independent
Infinitely many solutions is consistent - dependent
System with no solution:
is called Inconsistent.
EX2.
EX3.
Consistent
Independent
(Intersecting)
Consistent
Dependent
(Same graph)
EX4.
Inconsistent
(Parallel)

5. Practice Graphing
Solve the system by graphing. Then classify the system as consistent and independent, consistent and dependent, or inconsistent.
-2x +y = 5
y = -x +2
2. 3x - 2y = 10
3x - 2y = 22
2x + 5y = 6
4x +10y = 12
Infinitely many solution; Consistent and dependent
(-1,3) Consistent and independent
No solution; inconsistent

6. Graph systems of Linear Inequalities
To graph a system of linear inequalities, follow these steps:
Step 1 – Solve each inequality for y.
Step 2 – Graph each inequality.
Pick the type of lines (solid or dotted)
Pick where to shade (above or below)
Step 3 – Identify the region of the graph that is shaded for ALL of the inequalities

7. Solve the system of Inequalities by graphing4.

8. Practice systems of inequalities5. 6.