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 are the two main methods for solving systems of equations?

Back

The two main methods for solving systems of equations are substitution and elimination.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How does the substitution method work?

Back

In the substitution method, one equation is solved for one variable, and then that expression is substituted into the other equation(s) to solve for the remaining variables.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How does the elimination method work?

Back

In the elimination method, equations are manipulated (by addition or subtraction) to eliminate one variable, allowing the remaining variables to be solved.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean for a system of equations to be consistent?

Back

A consistent system of equations has at least one solution, meaning the equations intersect at one or more points.

Tags

CCSS.8.EE.C.8B

Front

What does it mean for a system of equations to be inconsistent?

Back

An inconsistent system of equations has no solution, meaning the equations represent parallel lines that never intersect.

Tags

CCSS.8.EE.C.8B

Front

What is a dependent system of equations?

Back

A dependent system of equations has infinitely many solutions, meaning the equations represent the same line.

Tags

CCSS.8.EE.C.8B

Front

What is the significance of the solution (3, 3, -4) in a 3-variable system?

Back

The solution (3, 3, -4) indicates the values of the three variables that satisfy all equations in the system.

Front

How can word problems be translated into systems of equations?

Back

Word problems can be translated into systems of equations by identifying the variables, writing equations based on the relationships described, and ensuring all conditions are represented.

Tags

CCSS.8.EE.C.8C

Front

What is the first step in solving a word problem involving a system of equations?

Back

The first step is to define the variables that represent the unknown quantities in the problem.

Tags

CCSS.8.EE.C.8C