Solutions to Equations Word Problems

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What is a system of equations?

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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 in the system.

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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 express the total or combined quantities.

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What does it mean if two variables are directly related in a word problem?

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If two variables are directly related, an increase in one variable results in a proportional increase in the other variable.

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What does it mean if two variables are inversely related in a word problem?

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If two variables are inversely related, an increase in one variable results in a proportional decrease in the other variable.

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How do you find the total from a word problem involving two people?

Back

Add the quantities prepared or worked on by each person to find the total.

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.

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What does the term 'fewer than' indicate in a word problem?

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'Fewer than' indicates subtraction; it means to take away a certain number from another quantity.

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How do you express 'three times' a variable in an equation?

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'Three times' a variable is expressed as 3 times the variable, e.g., if the variable is c, it is written as 3c.

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What is the significance of the total in a word problem?

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The total provides a constraint that helps to form one of the equations in the system.

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How do you interpret the phrase 'together they prepared'?

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This phrase indicates that the sum of the quantities from both subjects equals a specific total.