Systems

Front

What are parallel lines?

Back

Parallel lines are lines in a plane that never intersect and have the same slope.

Front

What does it mean if two lines have the same slope?

Back

If two lines have the same slope, they are parallel and will never meet.

Front

What is the elimination method in solving systems of equations?

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 substitution method in solving systems of equations?

Back

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

Front

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

Back

A system of equations has no solution if the lines represented by the equations are parallel and never intersect.

Front

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

Back

A system of equations has infinitely many solutions if the equations represent the same line, meaning they intersect at every point on that line.

Front

How do you determine the solution of a system of equations graphically?

Back

The solution of a system of equations can be determined graphically by finding the point(s) where the lines intersect.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation of a system of equations consists of the lines corresponding to each equation plotted on a coordinate plane.

Front

What is the first step in solving a system of equations by elimination?

Back

The first step is to align the equations so that corresponding variables and constants are in the same columns.

Front

What is the first step in solving a system of equations by substitution?

Back

The first step is to solve one of the equations for one variable in terms of the other variable.