Algebra 1 Chapter 5 Vocab Words
inconsistent system
y = 2x + 5-2x + y = -2 Linear Equations The system of equations is it consistent, dependent, independent, or none or of the above Graph each system of equations and describe it as consistent and independent, consistent and dependent, inconsistent, or none of these. 9x-6y=1 3x-2y=21.
system of linear inequality
"Solving" systems of linear inequalities means "graphing each individual inequality, and then finding the overlaps of the various solutions". So I graph each inequality, and then find the overlapping portions of the solution regions.
solution of a system of equations or inequalities
A "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 of linear equations or inequality
A "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.
system of linear equations
A "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.
independent system
Definition: A consistent system of linear equations with only one solution.
dependent system
If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line. If a system has no solution, it is said to be inconsistent . The graphs of the lines do not intersect, so the graphs are parallel and there is no solution.
linear inequality in two variables
The solution of a linear inequality in two variables like Ax + By > C is an ordered pair (x, y) that produces a true statement when the values of x and y are substituted into the inequality. Example: Is (1, 2) a solution to the inequality \\ 2x+3y>1 \\\\2\cdot 1+3\cdot 2\overset{?}{>}1 \\2+5\overset{?}{>}1 \\7>1 \\ The graph of an inequality in two variables is the set of points that represents all solutions to the inequality. A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality. The boundary line is dashed for > and < and solid for ≤ and ≥. The half-plane that is a solution to the inequality is usually shaded.
consistent system
When discussing the different methods of solving systems of equations, we only looked at examples of systems with one unique solution set. These are known as Consistent systems of equations but they are not the only ones. Three variable systems of equations with infinitely many solution sets are also called consistent