Systems of Linear Equations (Two Variables)

Front

What is a system of linear equations?

Back

A set of two or more linear equations with the same variables.

Front

What does it mean for a solution to a system of linear equations?

Back

A solution is an ordered pair (x, y) that makes all equations in the system true.

Front

What is the graphical representation of a system of linear equations?

Back

The graphs of the equations, which can intersect at one point, be parallel, or be the same line.

Front

What does it mean if two lines are parallel in a system of linear equations?

Back

The system has no solution because the lines never intersect.

Front

What does it mean if two lines coincide in a system of linear equations?

Back

The system has infinitely many solutions because every point on the line is a solution.

Front

How do you solve a system of linear 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 linear equations by elimination?

Back

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

Front

What is the point of intersection of two lines?

Back

The point where the graphs of the equations meet, representing the solution to the system.

Front

What is the slope-intercept form of a linear equation?

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the standard form of a linear equation?

Back

Ax + By = C, where A, B, and C are constants.