Systems of equations: FAQ

A system of equations is a set of two or more equations that all use the same variables. We can try to solve the system by finding values for the variables that make all of the equations true at the same time.

Practice with our Solutions of systems of equations exercise.

Systems of equations can be used to model lots of different situations. For example, if we're trying to figure out how many adult and child tickets were sold at a movie theater, we might set up a system of equations with one equation for the total number of tickets and another equation for the total amount of money collected. We could also use systems of equations to model things like mixtures of solutions, distances and speeds of moving objects, or costs and quantities of different items.

Practice with our Creating systems in context exercise.

Both substitution and elimination are methods for solving systems of equations. With substitution, we isolate one of the variables in one of the equations and then substitute that variable into the other equation. With elimination, we add or subtract the two equations in order to eliminate one of the variables.

Practice with our Systems of equations with substitution exercise.

Practice with our Systems of equations with elimination exercise.

Yes! A system of linear equations can have no solutions, one solution, or infinitely many solutions. Sometimes we can tell from looking at the system, and other times we may need to use substitution, elimination, or graphing to figure it out.

Practice with our Number of solutions to a system of equations graphically exercise.

Practice with our Number of solutions to a system of equations algebraically exercise.