Exam 8: Systems of Equations and Inequalities

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Perform the indicated operation, if possible. Do not use a calculator. If the operation cannot be completed, state why. Perform the indicated operation, if possible. Do not use a calculator. If the operation cannot be completed, state why.   2A - 3B 2A - 3B

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Identify the equation and variable that makes the substitution method easiest to use. Then solve the system. Identify the equation and variable that makes the substitution method easiest to use. Then solve the system.

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Solve the system of inequalities by graphing the solution region. Solve the system of inequalities by graphing the solution region.

(Essay)
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Form the augmented matrix, then name the diagonal entries of the coefficient matrix. Form the augmented matrix, then name the diagonal entries of the coefficient matrix.

(Multiple Choice)
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Find the area of the triangle with vertices (-1, -2), (4, 2), and (1, -2). Assume area units are cm2.

(Multiple Choice)
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Solve the system by graphing. If the solution does not appear to be a lattice point, estimate the solution to the nearest tenth (indicate that your solution is an estimate) Solve the system by graphing. If the solution does not appear to be a lattice point, estimate the solution to the nearest tenth (indicate that your solution is an estimate)

(Essay)
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Solve the system using the elimination method. Solve the system using the elimination method.

(Multiple Choice)
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Use a calculator to find A-1. Use a calculator to find A<sup>-1</sup>.

(Essay)
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Use the following to answer questions : Esther wants to spend no more than $60 buying gifts for her friends Barb and Wanda. She wants to spend at least $20 on Wanda's gift. -Solve the system of linear inequalities.

(Multiple Choice)
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Write the determinants D, Dx, Dy, and Dz for the system, then determine if a solution using Cramer's rule is possible by computing the value of D without the use of a calculator (do not solve the system). Write the determinants D, D<sub>x</sub>, D<sub>y</sub>, and D<sub>z</sub> for the system, then determine if a solution using Cramer's rule is possible by computing the value of D without the use of a calculator (do not solve the system).

(Essay)
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Solve the system using the elimination method. If the system is inconsistent or dependent, so state. Solve the system using the elimination method. If the system is inconsistent or dependent, so state.

(Multiple Choice)
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Solve using the elimination method. If the system is inconsistent or dependent, so state. For a system with linear dependence, write the answer in terms of a parameter. For coincident dependence, state the solution in set notation. Solve using the elimination method. If the system is inconsistent or dependent, so state. For a system with linear dependence, write the answer in terms of a parameter. For coincident dependence, state the solution in set notation.

(Multiple Choice)
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Solve the system of inequalities by graphing the solution region. Solve the system of inequalities by graphing the solution region.

(Essay)
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Solve the linear inequality by shading the appropriate half plane. 2x + 3y > 6

(Essay)
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Solve using the elimination method. If the system is inconsistent or dependent, so state. For a system with linear dependence, write the answer in terms of a parameter. For coincident dependence, state the solution in set notation. Solve using the elimination method. If the system is inconsistent or dependent, so state. For a system with linear dependence, write the answer in terms of a parameter. For coincident dependence, state the solution in set notation.

(Short Answer)
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Perform the indicated operation, if possible. Do not use a calculator. If the operation cannot be completed, state why. Perform the indicated operation, if possible. Do not use a calculator. If the operation cannot be completed, state why.   AB AB

(Short Answer)
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Substitute the x- and y-values indicated by the ordered pair (9, -5) to determine if it solves the system. Substitute the x- and y-values indicated by the ordered pair (9, -5) to determine if it solves the system.

(Multiple Choice)
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Solve the system by graphing. If the solution does not appear to be a lattice point, estimate the solution to the nearest tenth (indicate that your solution is an estimate). Solve the system by graphing. If the solution does not appear to be a lattice point, estimate the solution to the nearest tenth (indicate that your solution is an estimate).

(Essay)
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Decompose the rational expression into partial fractions. Decompose the rational expression into partial fractions.

(Essay)
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Perform the indicated operation, if possible. Do not use a calculator. Perform the indicated operation, if possible. Do not use a calculator.   A<sup>2</sup> A2

(Multiple Choice)
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