A1 Vocabulary Systems of Linear Equations & Inequalities

Front

Linear equation in two variables

Back

a relationship with a constant rate of change represented by a graph that forms a straight line

Front

Linear inequality in two variables

Back

a relationship with a constant rate of change represented by a solution set denoted by the graph of a line, that may or may not be included in the solution, and the set of points above or below the line.

Front

Solution

Back

The Coordinate Pair (x,y) that is true for all equations in a system. Where linear equations cross on the graph.

Front

One Solution

Back

when the system of equations have different slopes and cross at a single point (the solution).

Front

No Solution

Back

When a system of equations has equations that are parallel and never intersect and have the same slope.

Front

Infinite Solutions

Back

a system of equations in which all values are true (the equations are the same line). AKA All real numbers, all solutions, or infinitely many solutions.

Front

Solve by Graphing

Back

Graph two linear equations to find their point of intersection.

Front

Solve by Substitution

Back

solve one linear equation for x or y and then plug the expression x or y is equal to into the other equation and solve for the variable. Then plug in the solution for the variable into one of the original equations to solve for the other variable. Answer as a coordinate (x,y)

Front

Solve by Elimination

Back

Multiply everything in one linear equation by a number that will cancel either the x or y term when the two equations are combined.

Front

Parallel lines

Back

lines in the same plane that do not intersect and remain equidistant from one another.