Which statements are true for solutions when there is a system of two linear equations in two variables? Select all that apply. A. There are two solutions for a system that consists of two linear equations.
B. The points of intersection satisfy both the linear equations.
C. The intersections of their graphs correspond to their solutions.
D. The parallel lines will never have a solution.

A system of linear equations consists of two or more linear equations made up of two or more variables, such that all equations in the system are considered simultaneously.

To find the unique solution to a system of linear equations, we must find a numerical value for each variable in the system that will satisfy all equations in the system at the same time.

In order for a linear system to have a unique solution, there must be at least as many equations as there are variables.

The solution to a system of linear equations in two variables is any ordered pair  

(

x

,

y

)

that satisfies each equation independently. Graphically, solutions are points at which the lines intersect.

Key Terms

system of linear equations: A set of two or more equations made up of two or more variables that are considered simultaneously.

dependent system: A system of linear equations in which the two equations represent the

same line; there are an infinite number of solutions to a dependent system.

inconsistent system: A system of linear equations with no common solution because they

represent parallel lines, which have no point or line in common.

independent system: A system of linear equations with exactly one solution pair  

(

x

,

y

)

.

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