CL - Alg. 2 - Mod. 1 - Topic 1 Test

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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 simultaneously.

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How do you solve a system of equations using matrices?

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To solve a system of equations using matrices, you can represent the system in matrix form (AX = B) and then use methods like Gaussian elimination or finding the inverse of A (if it exists) to find the solution vector X.

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What does it mean to graph an inequality?

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Graphing an inequality involves shading a region of the graph that represents all the solutions to the inequality. The boundary line is either solid (for ≤ or ≥) or dashed (for < or >).

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What is the difference between a solid and dashed line in graphing inequalities?

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A solid line indicates that points on the line are included in the solution (≤ or ≥), while a dashed line indicates that points on the line are not included ( < or >).

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What is the meaning of the term 'shading' in graphing inequalities?

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Shading in graphing inequalities indicates the set of all possible solutions. The direction of shading depends on the inequality sign.

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How do you set up a system of equations from a word problem?

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Identify the variables, translate the relationships and conditions into equations, and ensure the equations represent the total or constraints given in the problem.

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What is the purpose of using variables in equations?

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Variables represent unknown quantities in equations, allowing us to formulate relationships and solve for these unknowns.

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What does it mean when twice as many cookies are sold at one price compared to another?

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It means that if you let x represent the number of cookies sold at the lower price, then the number sold at the higher price can be expressed as x/2.

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How do you interpret the solution of a system of equations?

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The solution of a system of equations represents the point(s) where the equations intersect, indicating the values of the variables that satisfy all equations.

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What is the significance of the coefficients in a system of equations?

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Coefficients indicate the relationship between the variables in the equations. They affect the slope and position of the lines when graphed.