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 if a system of equations has one solution?

Back

The lines representing the equations intersect at exactly one point.

Front

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

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

The lines representing the equations 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 graphical representation consists of lines or curves on a coordinate plane.

Front

What is the solution to the system: 2x + 3y = 6 and 4x - y = 5?

Back

(2, 0)

Front

What is the solution to the system: x + y = 5 and x - y = 1?

Back

(3, 2)

Front

What is the solution to the system: 3x + 2y = 12 and 6x + 4y = 24?

Back

Infinite solutions.