  # MTH 237 LINEAR ALGEBRA

Definition

A solution to a system of two linear equations with two unknowns is an ordered pair that makes each of
the equations true .

Examples

Decide whether or not the given ordered pairs are solutions to the system of equations: Is (5,−1) a solution to the system ?  Is (−1,3) a solution to the system?  Solve each system of equations by graphing the two linear equations and finding the point(s) they
have in common . Make sure that you check your solution before stating your conclusion.     A system can have exactly one solution. In this case, the system is called
consistent and the equations are called independent. This happens
x when the two equations graph to lines that intersect at a single point. A system can have an “ infinite number ” of solutions. In this case, the
system is called consistent and the equations are called dependent.
x This happens when the two equations graph to the same line A system can have no solution. In this case, the system is called
inconsistent and the equations are called independent. This happens
x when the two equations graph to parallel lines .

Examples

For each system, write both equations in slope - intercept form and decide – without graphing –
whether the system is consistent or inconsistent and whether the equations are dependent or  Find the solution to the system of equations  Prev Next

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