Systems of Equations Elimination (Easy)

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 set of values that satisfy all equations simultaneously.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean to solve a system of equations by elimination?

Back

Solving by elimination 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 elimination method used for?

Back

The elimination method is used to find the values of variables in a system of equations by eliminating one variable at a time.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

If a system has no solution, it means the equations represent parallel lines that never intersect.

Tags

CCSS.8.EE.C.8A

Front

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

Back

If a system has infinitely many solutions, it means the equations represent the same line, and there are countless points of intersection.

Tags

CCSS.8.EE.C.8B

Front

How do you determine if two equations are dependent?

Back

Two equations are dependent if they represent the same line, meaning one equation can be derived from the other by multiplication or division.

Tags

CCSS.8.EE.C.8B

Front

What is the first step in solving a system of equations by elimination?

Back

The first step is to align the equations so that corresponding variables and constants are in the same columns.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How can you manipulate equations to facilitate elimination?

Back

You can multiply one or both equations by a constant to create coefficients that are opposites, allowing for easy elimination.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

Coefficients determine the slope and position of the lines represented by the equations, affecting their intersection.

Tags

CCSS.8.EE.C.8A

Front

What is a consistent system of equations?

Back

A consistent system has at least one solution, meaning the lines intersect at one point or are the same line.

Tags

CCSS.8.EE.C.8A