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

How do you solve a system of equations by graphing?

Back

To solve a system of equations by graphing, plot each equation on the same coordinate plane. The point where the lines intersect represents the solution to the system.

Tags

CCSS.8.EE.C.8B

Front

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

Back

A consistent system of equations has at least one solution. This can be either one unique solution or infinitely many solutions.

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 lines represented by the equations do not intersect.

Tags

CCSS.8.EE.C.8B

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the elimination method in solving systems of equations?

Back

The elimination method 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

Define the term 'dependent' in the context of systems of equations.

Back

Dependent equations are equations that represent the same line, resulting in infinitely many solutions.

Tags

CCSS.8.EE.C.8B

Front

Define the term 'independent' in the context of systems of equations.

Back

Independent equations are equations that represent different lines, resulting in exactly one solution.

Tags

CCSS.8.EE.C.8B

Front

Back

The solution can be found by graphing both equations and identifying the intersection point, which is (3, 0).

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 and conditions into equations, and ensure the equations represent the same scenario.

Tags

CCSS.8.EE.C.8C