WU: Solving Systems 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 two lines to intersect on a graph?

Back

It means that the two equations have a common solution (x, y) that satisfies both equations.

Front

What is the graphical representation of a system with no solution?

Back

Two parallel lines that never intersect.

Front

What is the graphical representation of a system with one solution?

Back

Two lines that intersect at exactly one point.

Front

What is the graphical representation of a system with infinitely many solutions?

Back

Two lines that lie on top of each other (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 solution to the system of equations 2x + 3y = 6 and x - y = 1?

Back

(3, 0) is the solution.

Front

What does it mean if a system of equations has no solution?

Back

It means the equations represent parallel lines that do not intersect.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

It means the equations represent the same line.