Solving 3-variable systems REVIEW

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 to the system is the set of values that satisfy all equations simultaneously.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

A system has infinitely many solutions when the equations represent the same line or plane, meaning there are countless points that satisfy all equations.

Tags

CCSS.8.EE.C.8B

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 remaining variables.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the substitution method in solving systems of equations?

Back

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

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

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

Tags

CCSS.8.EE.C.8B

Front

What is the geometric interpretation of a system of three equations in three variables?

Back

The geometric interpretation involves visualizing the equations as planes in three-dimensional space, where the solution is the point of intersection of the planes.

Front

What is a unique solution in the context of systems of equations?

Back

A unique solution occurs when the equations intersect at exactly one point, meaning there is one set of values that satisfies all equations.

Tags

CCSS.8.EE.C.8A

Front

How can you check your solution to a system of equations?

Back

You can check your solution by substituting the values back into the original equations to see if they hold true.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the role of coefficients in a system of equations?

Back

Coefficients determine the slope and position of the lines or planes represented by the equations, affecting the nature of the solutions.

Tags

CCSS.8.EE.C.8B

Front

What is a dependent system of equations?

Back

A dependent system is one where the equations are not independent, meaning one equation can be derived from another, leading to infinitely many solutions.

Tags

CCSS.8.EE.C.8B