Solving Systems of Equations

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

The three main methods are: 1) Graphing, 2) Substitution, 3) Elimination.

Substitution is best when one equation is easily solvable for one variable, allowing for straightforward substitution into the other equation.

Graphing a system of equations involves plotting each equation on the same coordinate plane to visually identify the point(s) of intersection, which represent the solution.

To use elimination, you manipulate the equations to eliminate one variable, allowing you to solve for the other variable.

The solution to a system of equations is the set of values for the variables that satisfy all equations in the system simultaneously.

The point of intersection represents the solution to the system of equations, indicating the values of the variables that satisfy both equations.

You can check a solution by substituting the values back into the original equations to see if they hold true.

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable.

A consistent system has at least one solution, meaning the equations intersect at one or more points.