System Word Problems - Setting Up

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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 point(s) where the equations intersect.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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How do you represent a cost problem with a system of equations?

Back

You can represent a cost problem by defining variables for the unknowns (e.g., number of items) and writing equations based on the relationships given in the problem.

Tags

CCSS.8.EE.C.8C

Front

What does the slope represent in a linear equation?

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The slope represents the rate of change of the dependent variable with respect to the independent variable. In cost problems, it often represents the cost per item.

Tags

CCSS.8.EE.B.5

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What is the y-intercept in a linear equation?

Back

The y-intercept is the value of y when x is 0. It represents the fixed cost or starting value in cost problems.

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How do you set up a system of equations for two different pricing models?

Back

Define variables for the unknowns, write an equation for each pricing model, and set them equal to each other if comparing costs.

Tags

CCSS.HSA.CED.A.3

Front

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

Back

The first step is to express both equations in a standard form, usually y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How can you determine the number of solutions in a system of equations?

Back

You can determine the number of solutions by analyzing the slopes of the lines: if they are the same, there are infinitely many solutions; if they intersect, there is one solution; if they are parallel, there are no solutions.

Tags

CCSS.8.EE.C.8B

Front

What is the significance of the fixed cost in a cost equation?

Back

The fixed cost is the initial amount charged regardless of the quantity purchased, representing costs that do not change with the number of items.

Tags

CCSS.8.EE.B.5

Front

How do you interpret the solution of a system of equations in a real-world context?

Back

The solution represents the values of the variables that satisfy all equations in the system, often indicating quantities of items or costs that make two scenarios equal.

Tags

CCSS.8.EE.C.8C

Front

What is a common method for solving systems of equations?

Back

Common methods include substitution, elimination, and graphing.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6