Systems of Linear Equations Vocabulary and Key Concepts

Ordered Pair

A pair of numbers that can be used to locate a point on a coordinate plane

Solution to a System of Linear Equations

A pair of values that satisfies all the equations in the system

Linear

A relationship or function that can be represented by a straight line

Define Infinite solution System

A system has infinite solutions if the equations have the same slope and the same y-intercept. The graphs coincide so every point is a solution.

Define No solution System

A system has no solutions 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.

Define One Solution

A system has on solution if the equations have different slopes. The graphs of the two lines will intersect. The point of intersection represents to solution.

The method of eliminating one variable by adding or subtracting two equations with a common term is called the _____________ method.

Elimination

You can solve a system of linear equations using the graphical method by finding the point of ______________ .

Intersection

When the graph of a system of equations has an infinite number of solutions, the lines are _________________

Parallel

5.2 You are given a system of equations to solve. Identify a condition of one or both of the equations that might persuade you to use either the elimination method or the substitution method. Explain.

Possible answer: If both equations share a common term, use the elimination method. If one equation has a variable isolated on one side, use the substitution method to substitute the expression for the isolated variable into the other equation.

5.4 Explain why the solution to a system of two linear equations is represented by the point of intersection of the graphs of the equations.

Possible answer: The graph of a linear equation represents all the solutions of the equation. When you have a system of equations, all the solutions of each equation are represented by lines. The only solution that satisfies both equations will be a point that lies on both lines, at their intersection.

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

List the three types of SOLUTIONS to a linear system of equations that you have studied. Describe the graph of each type.

The graph of a system with a one solution is two intersecting lines. The graph of an no solution is two parallel lines. The graph of a infinitely many solutions is a single line.

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 equations may be solved geometrically using the...

graphical method.

A system of linear equations can have ________ solution, no solution, or infinitely many solutions.

one

A system of linear equations may have _________, ___________, or ____________.

one solution (point of intersection), no solution (parallel lines), or infinite many solutions (the lines formed are on top of one another).

A system of linear equations consists of linear equations with more than one ____________ .

variable