Flashcard - Systems of Equations

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope and will never intersect.

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1.

Front

What is the solution to a system of equations?

Back

The solution to a system of equations is the ordered pair (x, y) that satisfies all equations in the system.

Front

How do you solve a system of equations using substitution?

Back

To solve using substitution, solve one equation for one variable, then substitute that expression into the other equation.

Front

How do you solve a system of equations using elimination?

Back

To solve using elimination, 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 is the intersection points of the lines represented by the equations.

Front

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

Back

Front

Back

The y-intercept is 3, which is the point where the line crosses the y-axis.

Front

How can you determine if a system of equations has no solution?

Back

A system has no solution if the lines are parallel, meaning they have the same slope but different y-intercepts.