TAKS TAKS Objective 4Linear Equations and

Inequalities

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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