Systems of Equations Word Problems

Front

What is a system of equations?

Back

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

Front

What does it mean for a system of equations to have one solution?

Back

The lines intersect at exactly one point.

Front

What does it mean for a system of equations to have no solution?

Back

The lines are parallel and never intersect.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

The lines coincide, meaning they are the same line.

Front

How do you solve a system of equations using substitution?

Back

Solve one equation for one variable and substitute that expression into the other equation.

Front

How do you solve a system of equations using elimination?

Back

Add or subtract the equations to eliminate one variable, then solve for the remaining variable.

Front

What is the graphical representation of a system of equations?

Back

The solution is represented by the point(s) where the lines intersect.

Front

If two lines are parallel, what can be said about their slopes?

Back

The slopes of parallel lines are equal.

Front

What is the first step in solving a word problem involving a system of equations?

Back

Define the variables and what they represent.

Front

How can you check your solution to a system of equations?

Back

Substitute the solution back into the original equations to see if they hold true.