Solving Systems with 3 Variables

Front

What is a system of equations with 3 variables?

Back

A set of equations that have three different variables, which can be solved simultaneously to find the values of those variables.

Front

What does it mean to solve a system of equations?

Back

To find the values of the variables that satisfy all equations in the system at the same time.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is an ordered triple?

Back

A set of three elements in a specific order, typically representing the values of three variables in a solution.

Front

How do you represent the solution of a system of equations with 3 variables?

Back

The solution is represented as an ordered triple (x, y, z), where x, y, and z are the values of the variables.

Front

What is the first step in solving a system of equations with 3 variables?

Back

Choose one equation and solve for one variable in terms of the others.

Front

What is substitution in the context of solving systems of equations?

Back

Substitution is a method where you solve one equation for a variable and then substitute that expression into the other equations.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is elimination in the context of solving systems of equations?

Back

Elimination is a method where you add or subtract equations to eliminate one variable, making it easier to solve for the others.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

It means that the equations represent parallel planes that do not intersect at any point.

Tags

CCSS.8.EE.C.8B

Front

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

Back

It means that the equations represent the same plane or coincide in some way, leading to multiple intersection points.

Tags

CCSS.8.EE.C.8B

Front

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

Back

Substitute the values of the variables back into the original equations to see if they hold true.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6