Day 6

inconsistent system

a system of equations or inequalities that has no common solution because they represent parallel lines, which have no point or line in common.

independent system

a system of equations with a single solution

dependent system

a system of linear equations in which the two equations represent the same line; there are infinite number of solutions to a dependent system.

consistent system

if a system has at least one solution, if it has exactly one solution, it's independent but if the consistent system has infinite number of solutions its dependent.

solutions of system of inequalities

is the ordered paired that is a solution to all inequalities in the system and the graph of the linear inequality is the graph of all solutions of the system.

solve by elimination

the elimination method is where you actually eliminate one of the variables by adding two equations. you eliminate one variable so you can solve for the other variable. in a two-equation system, since you have two variables, eliminating one makes the solving easier.

at least

the smallest possible number in a set or sequence

solve by graphing

to solve a linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be in the point where the two lines intersect.

system of linear equations

two or more linear equations

system of linear inequalities

two variables consists of at least two linear inequalities in the same variable. the solution of a linear inequality is the ordered paired that is that solution to all inequalities in the system and the graph of the linear inequality is the graph of all solutions of the system

solution of a system of equations

usually has one solution(graphs intersect at one point), but sometimes it can have no solution(parallel lines) or infinite solutions (same line)

at most

when a number is at most, they are less than or equal, but not greater

analysis statements

when analyzing weather the equation is the solution,no solution, or infinite many solutions.

solve by substitution

works by solving one of the equations for one of the variables, and then plugging this back into the other equation, "substituting" for the chosen variable and solving the other. then you back-solve for the first variable.