Word Problems (system of equations)

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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

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

Back

Identify the variables, translate the relationships and conditions into equations, and ensure the equations reflect the problem's constraints.

Tags

CCSS.HSA.CED.A.3

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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 make all equations in the system true.

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

What is the graphical method for solving systems of equations?

Back

The graphical method involves graphing each equation on the same coordinate plane and identifying the point(s) where the graphs intersect.

Tags

CCSS.8.EE.C.8B

Front

What are the possible outcomes when solving a system of equations?

Back

1. One unique solution (the lines intersect at one point). 2. No solution (the lines are parallel). 3. Infinitely many solutions (the lines coincide).

Tags

CCSS.8.EE.C.8B

Front

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

Back

Substitute the values of the variables back into the original equations to verify that both equations are satisfied.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is a word problem?

Back

A word problem is a mathematical problem presented in a narrative form, requiring interpretation and translation into mathematical expressions.

Tags

CCSS.HSA-SSE.A.1A

Front

What is the importance of defining variables in word problems?

Back

Defining variables helps clarify what each quantity represents, making it easier to translate the problem into equations.

Tags

CCSS.HSA-SSE.A.1A