Systems of Equations - Word Problems

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.

To solve a system of equations means to find the values of the variables that satisfy all equations in the system simultaneously.

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

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

Identify the variables, translate the relationships and conditions into equations, and ensure the equations represent the same situation.

Defining variables helps clarify what each variable represents, making it easier to set up equations and solve the problem.

Substitute the solution back into the original equations to verify that both equations are satisfied.

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

An inconsistent system has no solutions, meaning the equations represent parallel lines that never intersect.

A dependent system has infinitely many solutions, meaning the equations represent the same line.