Presentation is loading. Please wait.

Presentation is loading. Please wait.

Solving Systems with 2 Variables U3.1. Vocabulary A system of linear equations in two variables x and y, also called a linear system, consists of two.

Similar presentations


Presentation on theme: "Solving Systems with 2 Variables U3.1. Vocabulary A system of linear equations in two variables x and y, also called a linear system, consists of two."— Presentation transcript:

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 Example 1. Solve by graphing y = -x + 5 Solve by Graphing -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. Consistent Independent (Intersecting) Consistent Dependent (Same graph) Inconsistent (Parallel) EX2.EX3. EX4.

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

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 graphing 4.

8 Practice systems of inequalities 5.6.


Download ppt "Solving Systems with 2 Variables U3.1. Vocabulary A system of linear equations in two variables x and y, also called a linear system, consists of two."

Similar presentations


Ads by Google