solving systems of linear equations

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 if a system of equations has one solution?

Back

The lines intersect at exactly one point, representing a unique solution.

Front

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

Back

The lines are parallel and never intersect.

Front

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

Back

The lines coincide, meaning they are the same line.

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 graphical representation of a system of linear equations?

Back

The solution is represented by the point(s) where the lines intersect on a graph.

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

How can you determine if two lines are parallel?

Back

If they have the same slope but different y-intercepts.

Front

How can you determine if two lines are perpendicular?

Back

If the product of their slopes is -1.