A1: 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.

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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.

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What does it mean to 'break even' in a business context?

Back

Breaking even means that total revenue equals total costs, resulting in neither profit nor loss.

Front

How do you find the number of solutions to a system of equations?

Back

A system can have one solution (intersecting lines), no solution (parallel lines), or infinitely many solutions (same line).

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What is the importance of defining variables in word problems?

Back

Defining variables clarifies what each symbol represents, making it easier to set up equations and solve the problem.

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

Back

Substitute the solution back into the original equations to see if it satisfies all equations.

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What is the graphical representation of a system of equations?

Back

The graphical representation consists of lines or curves on a coordinate plane, where the intersection points represent the solutions.

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What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and substituting that expression into the other equation.

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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 other.

Front

How do you set up an equation from a word problem involving costs?

Back

Identify fixed costs and variable costs, then create an equation that represents total cost as a function of the number of items.