Lesson 19 Formulating a 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 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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Define variables in a word problem.

Back

Variables are symbols used to represent unknown quantities in mathematical expressions or equations, often denoted by letters such as x, y, or z.

Tags

CCSS.6.EE.B.6

Front

What does it mean to formulate a system of equations from a word problem?

Back

Formulating a system of equations involves translating the relationships and conditions described in a word problem into mathematical equations using variables.

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How do you represent the total number of items sold in a word problem?

Back

You can represent the total number of items sold by creating an equation that sums the quantities of each type of item, often set equal to the total.

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CCSS.HSA.CED.A.3

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What is the significance of defining relationships between variables in a system of equations?

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Defining relationships helps to create equations that express how the variables interact, which is essential for finding a solution to the system.

Tags

CCSS.8.EE.C.8B

Front

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

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The first step is to write down the equations based on the relationships described in the problem.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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How can you check if your solution to a system of equations is correct?

Back

You can check the solution by substituting the values back into the original equations to see if they hold 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 does it mean for a system of equations to be consistent?

Back

A consistent system has at least one solution, meaning the equations intersect at one or more points.

Tags

CCSS.8.EE.C.8B