# Algebra II w/ trig - PowerPoint PPT Presentation

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3.1 Solving Systems of Equations by Graphing 3.3 Solving Systems of Inequalities by Graphing 3.4 Linear Programming. Algebra II w/ trig. 3.1 Solving Systems of Equations by Graphing System of 2 linear equations (in 2 variables x and y) ---2 equations with 2 variables each

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Algebra II w/ trig

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## 3.1 Solving Systems of Equations by Graphing3.3 Solving Systems of Inequalities by Graphing3.4 Linear Programming

Algebra II w/ trig

• 3.1 Solving Systems of Equations by Graphing

System of 2 linear equations (in 2 variables x and y)

---2 equations with 2 variables each

---solution of a system: an ordered (x, y) that makes both equations true

• Solving a System Graphically

• Graph each equation on the same coordinate plane. (Use Graph Paper)

• If the lines intersect(different slope/different y-intercept): The point where the lines intersect is the solution. That solution is classified as consistent independent.

• If the lines do not intersect:

• They are the same line(same slope/same y-intercept)---IMS(they have every pt in common)—is classified as consistent dependent

• They are parallel lines(same slope/different y-intercept)---NO SOLUTION(no common points)---is classified as inconsistent

I. Graph the system of equations and describe it as consistent and independent, consistent and dependent, or inconsistent.

A.

B.C.

D.E.

• 3.3 Solving Systems of Inequalities by Graphing

• Steps for Graphing:

• Graph the lines and appropriate shading for each inequality on the same coordinate plane.

• Be sure to pay attention to whether the lines are dotted or solid.

• The final shaded area is the section where all the shadings overlap.

****** Sometimes it helps to use a different colored pencil for each line and shaded region. It makes it easier to determine the overlapped shaded regions.

II. Graph the systems of Inequalities:

A.B.

C.

D.

• 3.4 Linear Programming

• Graph each system of inequalities. Name the coordinates of the vertices of the feasible region. Name the maximum and minimum values of the given region. Name the polygon the shaded region forms.

• Y > 2x

y > 6-x

y < 6

f(x, y) – 4x + 3y

B. -3x + y > 2

y > -x -2

y -4 < x

f(x, y) = -3x +5y