Algebra House
  • Ask a Question
    • Answered Questions
  • Examples
  • State Test Practice
    • Algebra 1 State Test Practice
    • Geometry State Test Practice
  • ACT and SAT
  • Calculators
    • Problem Solver
    • Graphing Calculator
    • 3D Graphing Calculator
  • Contact
    • Contact Algebra House
    • Leave a Tip


​​ALGEBRA eXAMPLES

System of Inequalities

1/14/2013

0 Comments

 
How do you solve the system of inequalities by graphing?
y ≤ 2x + 2
y < -x + 1

Graph each inequality, then the solution would be the overlap of the two half-planes.

Picture
To graph y ≤ 2x + 2:

Graph the line y = 2x + 2  {y-intercept is 2 and slope is 2}

Use a solid line, given the less than or equal to sign.
This means the solution to this inequality also includes
the points on the boundary line

Since it is ≤, shade down the y-axis from the boundary line


Picture
To graph y < -x + 1:

Graph the line y = -x + 1  {y-intercept is 1 and slope is -1}

Use a dash line, given just the less than sign with no equal to.
This means the solution set to this inequality does not include
the points on the boundary line.

Since it is <, shade down the y-axis from the boundary line.


The solution to the system of inequalities {shown below} is the overlap of the two half-planes.


Picture
The solution set (overlap shown to the left) is the set of points that satisfies both inequalities.

- Algebra House

0 Comments

Your comment will be posted after it is approved.


Leave a Reply.


    Ask a Question


    Latest Video
    Picture


    Examples

    All
    All Word Problems
    Basic Math
    Combining Like Terms
    Distributive Property
    Equations Of Lines
    Exponents
    Factoring
    Foil Method
    Functions
    Geometry
    Graphing
    Imaginary Numbers
    Inequalities
    Linear Equations
    Literal Equations
    Miscellaneous
    Percents
    Pythagorean Theorem
    Quadratic Equations
    Radicals
    Simplifying
    Slopes And Intercepts
    Solving Equations
    System Of Equations
    Word Problems Age
    Word Problems Distance
    Word Problems Geometry
    Word Problems Integers
    Word Problems Misc.
    Word Problems Mixture
    Word Problems Money
    Word Problems Number



Algebra House
  • Ask a Question
    • Answered Questions
  • Examples
  • State Test Practice
    • Algebra 1 State Test Practice
    • Geometry State Test Practice
  • ACT and SAT
  • Calculators
    • Problem Solver
    • Graphing Calculator
    • 3D Graphing Calculator
  • Contact
    • Contact Algebra House
    • Leave a Tip