Systems of Linear Equations Vocabulary and Key Concepts
Define Unique Solution
A system has a unique solution if the equations have different slopes. The graphs of the two lines will intersect. The point of intersection represents to solution.
Define Dependent System
A system is dependent if the equations have the same slope and the same y-intercept. The graphs coincide so every point is a solution.
Define Inconsistent System
A system is inconsistent if the equations have the same slope but different intercepts. The graphs are parallel lines. Since there is no point of intersection, the system has no solution.
When a system of equations has an infinite number of solutions, it is called a(n) _______________ system
Dependent
The method of eliminating one variable by adding or subtracting two equations with a common term is called the _____________ method.
Elimination
When a system of equations has no solution, it is called a(n) ________________ system.
Inconsistent
You can solve a system of linear equations using the graphical method by finding the point of ______________ .
Intersection
A linear equation in the form ax + by = c is called the ___________ form of a linear equation.
Standard
The______________ method involves expressing one variable in terms of the other variable and substituting an expression into the other equation.
Substitution
A system of equations may be solved algebraically using...
The elimination method or the substitution method
When does the graphical method NOT good to use?
The graphical method is not good to use when the intersection point is not an integer. Graphing in this case would only provide an estimate.
A system of linear equations can have a(n) ________ solution, no solution, or infinitely many solutions.
Unique
A system of equations may be solved geometrically using the...
graphical method.
A system of linear equations may have _________, ___________, or ____________.
one solution (unique solution---point of intersection), no solution (inconsistent system---parallel lines), or infinite many solutions (dependent system---the lines formed are on top of one another).
A system of linear equations consists of linear equations with more than one ____________ .
variable