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 find the values of the 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 to eliminate one variable, allowing the remaining variable to be solved easily.

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 solutions, 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

How can you represent a word problem as a system of equations?

Back

To represent a word problem as a system of equations, identify the variables, translate the relationships and conditions into equations, and ensure all equations are aligned with the problem's context.

Tags

CCSS.HSA.CED.A.3

Front

What is the importance of checking your solution in a system of equations?

Back

Checking your solution ensures that the values satisfy all original equations, confirming that the solution is correct.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the graphical interpretation of a system of equations?

Back

The graphical interpretation involves plotting the equations on a coordinate plane; the points of intersection represent the solutions to the system.

Tags

CCSS.8.EE.C.8B