Writing systems of Equations from word problems

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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

Front

How do you represent the perimeter of a rectangle in terms of its length and width?

Back

The perimeter P of a rectangle can be represented as P = 2l + 2w, where l is the length and w is the width.

Tags

CCSS.8.EE.C.7B

Front

What does it mean when a word problem states that one quantity is 'less than' another?

Back

It indicates a subtraction relationship. For example, if the length is '4 meters less than' three times the width, it can be expressed as l = 3w - 4.

Front

How can you express the total number of coins in a word problem involving different types of coins?

Back

You can express the total number of coins by using a variable for each type of coin and setting up an equation that sums them. For example, if p is pennies and n is nickels, then p + n = total number of coins.

Tags

CCSS.HSA.CED.A.3

Front

What is the relationship between the number of animals and their legs in a barn problem?

Back

The relationship can be expressed using a system of equations where one equation represents the total number of animals and another represents the total number of legs. For example, x + y = total animals and 4x + 2y = total legs.

Front

How do you set up an equation for total revenue from ticket sales?

Back

You can set up an equation by multiplying the price of each type of ticket by the number of tickets sold and summing them. For example, if x is adult tickets and y is student tickets, the equation would be 4.50x + 2.50y = total revenue.

Tags

CCSS.HSA.CED.A.3

Front

What is the significance of defining variables in word problems?

Back

Defining variables helps to translate the problem into mathematical equations, making it easier to solve for unknown quantities.

Tags

CCSS.6.EE.B.6

Front

How do you determine the number of equations needed in a system?

Back

The number of equations needed typically corresponds to the number of variables you are trying to solve for. For example, to find two unknowns, you need at least two equations.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

The first step is to write the system of equations based on the information provided in the word problem.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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