Systems of Equations - word problems

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 point(s) where the equations intersect.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean to solve a system of equations?

Back

To solve a system of equations means to find the values of the variables that satisfy all equations in the system simultaneously.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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

How can word problems be represented as 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 using the information given.

Tags

CCSS.8.EE.C.8C

Front

What is a variable in the context of equations?

Back

A variable is a symbol (often x or y) that represents an unknown value in an equation.

Tags

CCSS.6.EE.A.2B

Front

What does it mean for two equations to be consistent?

Back

Two equations are consistent if they have at least one solution (they intersect at one or more points).

Tags

CCSS.8.EE.C.8B

Front

What does it mean for two equations to be inconsistent?

Back

Two equations are inconsistent if they have no solutions (they are parallel and never intersect).

Tags

CCSS.8.EE.C.8A

Front

What is the graphical representation of a system of equations?

Back

The graphical representation of a system of equations is the plot of the equations on a coordinate plane, where the intersection points represent the solutions.

Tags

CCSS.8.EE.C.8B

Front

How do you check the solution of a system of equations?

Back

To check the solution, substitute the values of the variables back into the original equations to see if they hold true.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6