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 a solution to a system of equations?

Back

An ordered pair that satisfies all equations in the system.

Front

What is the graphical representation of a system of equations?

Back

The intersection points of the lines representing the equations.

Front

What are parallel lines in the context of systems of equations?

Back

Lines that never intersect and have no solution.

Front

What are intersecting lines in a system of equations?

Back

Lines that cross at one point, representing a unique solution.

Front

What are overlapping lines in a system of equations?

Back

Lines that lie on top of each other, representing infinitely many solutions.

Front

How do you solve a system of equations using substitution?

Back

Replace one variable with an expression from another equation.

Front

How do you solve a system of equations using elimination?

Back

Add or subtract equations to eliminate one variable.

Front

What is the solution to the system: y = 2x + 1 and y = 4x - 1?

Back

(1, 3)

Front

What is the solution to the system: y = -x + 2 and y = 3x - 4?

Back

(2, 0)