TAKS TAKS Objective 4 Linear Equations and Inequalities Join Spongebob in the sea of learning!
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Transcript of TAKS TAKS Objective 4 Linear Equations and Inequalities Join Spongebob in the sea of learning!
TAKS TAKS Objective 4Linear Equations and
Inequalities
Join Spongebob in the sea of learning!
System of Linear EquationsA “system” of equations is a set or collection of equations
that you deal with all together at once. Linear equations (ones that graph as straight lines) are simpler than non-linear equations, and the simplest linear system is one with two equations and two variables.
Solution(s) to the SystemAn ordered pair that is a solution of
each equation in the system.
One Solution
A point where two functions intersect once.
Example
• McPherson Rd. and Del Mar Blvd. intersect once.
No Solutions
When two(2) lines never intersect.
Example
7x+y=1328x+4y=-12↑This set of equations is an example of
no solution. The lines will never intersect.
Infinitely Many Solutions
When an equation is proven true for all real numbers.
Example
24x-27y=42-9y+8x=14↑These equations equal to infinite solutions.
Linear Inequality
A “system” of linear inequalities is a set of linear inequalities that you deal with all at once. Usually you start off with two or three linear inequalities.
Boundary (Restrictions)
Where a function or expression does not exceed.Divides the coordinate plane into two regions
Solution Set
A group of ordered pairs that satisfy the equation(s).
Consistent System
A system of equations that has at least one solution.
Inconsistent System
Dependent System
A consistent system of equations that has infinitely many solutions.
Example of Infinite Solutions
Independent System
A consistent system that has exactly one solution
Example of One Solution
Break-Even Point
The point at which costs and revenues are the same is sometimes called the break-even point.
Example of a Break Even Point
By: Shanthi Ayyadhury
Houston Academy for International Studies