Review System of Equations (E-Learning 1/6)

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 on a graph.

Tags

CCSS.8.EE.C.8B

Front

What does it mean if a system of equations has one solution?

Back

It means that the graphs of the equations intersect at exactly one point, indicating a unique solution for the variables.

Tags

CCSS.8.EE.C.8A

Front

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

Back

It means that the graphs of the equations are parallel and never intersect, indicating that there is no set of values for the variables that satisfies both equations.

Tags

CCSS.8.EE.C.8A

Front

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

Back

It means that the equations represent the same line, so every point on the line is a solution to the system.

Tags

CCSS.8.EE.C.8A

Front

How can you determine the number of solutions in a system of equations graphically?

Back

By graphing the equations and observing the number of intersection points: one point (one solution), no points (no solution), or infinitely many points (same line).

Tags

CCSS.8.EE.C.8B

Front

What is the substitution method for solving systems of equations?

Back

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

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the elimination method for solving systems of equations?

Back

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

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise over run).

Tags

CCSS.8.EE.B.5

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts, meaning they 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, indicating they intersect at a right angle.

Tags

CCSS.8.EE.B.6