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