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 system of equations to have a solution?

Back

It means there is at least one set of values for the variables that satisfies all equations in the system.

Front

What is the graphical representation of a system of equations?

Back

The graphs of the equations plotted on the same coordinate plane.

Front

What does it mean if two lines intersect on a graph?

Back

The system of equations has one unique solution.

Front

What does it mean if two lines are parallel on a graph?

Back

The system of equations has no solution.

Front

What does it mean if two lines are coincident on a graph?

Back

The system of equations has infinitely many solutions.

Front

How do you solve a system of equations by 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 by 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: y = 2x + 1 and y = 4x - 1?

Back

(1, 3)

Front

What is the solution to the system: y = 3x - 8 and y = 4 - x?

Back

(3, 1)