System of Equations - Substitution-Elimination-Graphing

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables that are solved simultaneously.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What are the three main methods for solving systems of equations?

Back

The three main methods are Substitution, Elimination, and Graphing.

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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the elimination method?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, allowing for the solution of the remaining variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

When is it best to use the graphing method to solve a system of equations?

Back

Graphing is best used when the equations are simple and can be easily plotted on a graph.

Tags

CCSS.8.EE.C.8B

Front

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

Back

A consistent system has at least one solution, meaning the lines 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 has no solutions, meaning the lines are parallel and never intersect.

Tags

CCSS.8.EE.C.8B

Front

What is a dependent system of equations?

Back

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

Tags

CCSS.8.EE.C.8B

Front

How do you write a system of equations from a word problem?

Back

Identify the variables, translate the relationships into equations, and ensure the equations represent the same context.

Tags

CCSS.8.EE.C.8C

Front

What is the first step in solving the system of equations 7x - y = -10 and -7x + 5y = -6 using elimination?

Back

The first step is to align the equations and decide which variable to eliminate by manipulating the equations.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6