system of equations

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 solution to a system of equations?

Back

A solution is a set of values for the variables that makes all equations true.

Front

How can you determine if a point is a solution to a system of equations?

Back

Substitute the point's coordinates into each equation to see if they hold true.

Front

What are natural numbers?

Back

Natural numbers are counting numbers: 1, 2, 3, 4, ... (not including zero).

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection point(s) of the lines representing the equations.

Front

What does it mean if two lines intersect at one point?

Back

It means the system has one unique solution.

Front

What does it mean if two lines are parallel?

Back

It means the system has no solution, as the lines never intersect.

Front

What does it mean if two lines coincide?

Back

It means the system has infinitely many solutions, as the lines are the same.

Front

How do you solve a system of equations by substitution?

Back

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

Front

How do you solve a system of equations by elimination?

Back

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