Systems of Equations

A set of two or more equations with the same variables.

Finding the values of the variables that satisfy all equations in the system.

A pair of numbers (x, y) that represents a point on the coordinate plane.

The point where the graphs of the equations intersect.

Substitute the point into each equation; if it satisfies all equations, it is a solution.

The lines or curves representing each equation plotted on the same coordinate plane.

The system has no solution because the lines never intersect.

The system has infinitely many solutions because the lines are the same.

Solving one equation for one variable and substituting that expression into the other equation.

Adding or subtracting equations to eliminate one variable, making it easier to solve.