Solving Linear Systems

Front

What is a linear system?

Back

A linear system is a collection of one or more linear equations involving the same variables.

Front

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

Back

A system has a unique solution if the equations intersect at exactly one point on the graph.

Front

What does it mean for a system of equations to have no solution?

Back

A system has no solution if the equations represent parallel lines that never intersect.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

A system has infinitely many solutions if the equations represent the same line, meaning they overlap completely.

Front

How can you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts.

Front

What is the substitution method for solving linear systems?

Back

The substitution method involves solving one equation for one variable and substituting that expression into the other equation.

Front

What is the elimination method for solving linear systems?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

What is the graphical method for solving linear systems?

Back

The graphical method involves graphing the equations on the same coordinate plane and identifying the point(s) of intersection.

Front

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

Back

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

Front

How do you find the intersection point of two lines algebraically?

Back

To find the intersection point, solve the system of equations simultaneously using substitution or elimination.