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