Solved: In 57 and 58, use properties of determinants to

In Problems 118, solve each system of equations using the method of substitution or the method of elimination. If the system has no solution, say that it is inconsistent.

In Problems 118, solve each system of equations using the method of substitution or the method of elimination. If the system has no solution, say that it is inconsistent.

In Problems 118, solve each system of equations using the method of substitution or the method of elimination. If the system has no solution, say that it is inconsistent.

In Problems 118, solve each system of equations using the method of substitution or the method of elimination. If the system has no solution, say that it is inconsistent.

In Problems 118, solve each system of equations using the method of substitution or the method of elimination. If the system has no solution, say that it is inconsistent.

In Problems 118, solve each system of equations using the method of substitution or the method of elimination. If the system has no solution, say that it is inconsistent.

In Problems 118, solve each system of equations using the method of substitution or the method of elimination. If the system has no solution, say that it is inconsistent.

In Problems 118, solve each system of equations using the method of substitution or the method of elimination. If the system has no solution, say that it is inconsistent.

In Problems 118, solve each system of equations using the method of substitution or the method of elimination. If the system has no solution, say that it is inconsistent.

In Problems 118, solve each system of equations using the method of substitution or the method of elimination. If the system has no solution, say that it is inconsistent.

In Problems 118, solve each system of equations using the method of substitution or the method of elimination. If the system has no solution, say that it is inconsistent.

In Problems 118, solve each system of equations using the method of substitution or the method of elimination. If the system has no solution, say that it is inconsistent.

In Problems 118, solve each system of equations using the method of substitution or the method of elimination. If the system has no solution, say that it is inconsistent.

In Problems 118, solve each system of equations using the method of substitution or the method of elimination. If the system has no solution, say that it is inconsistent.

In Problems 118, solve each system of equations using the method of substitution or the method of elimination. If the system has no solution, say that it is inconsistent.

In Problems 118, solve each system of equations using the method of substitution or the method of elimination. If the system has no solution, say that it is inconsistent.

In Problems 118, solve each system of equations using the method of substitution or the method of elimination. If the system has no solution, say that it is inconsistent.

In Problems 118, solve each system of equations using the method of substitution or the method of elimination. If the system has no solution, say that it is inconsistent.

In Problems 19 and 20, write the system of equations corresponding to the given augmented matrix.

In Problems 19 and 20, write the system of equations corresponding to the given augmented matrix.

In Problems 2128, use the following matrices to compute each expression.

In Problems 2128, use the following matrices to compute each expression.

In Problems 2128, use the following matrices to compute each expression.

In Problems 2128, use the following matrices to compute each expression.

In Problems 2128, use the following matrices to compute each expression.

In Problems 2128, use the following matrices to compute each expression.

In Problems 2128, use the following matrices to compute each expression.

In Problems 2128, use the following matrices to compute each expression.

In Problems 2934, find the inverse, if there is one, of each matrix. If there is not an inverse, say that the matrix is singular.

In Problems 2934, find the inverse, if there is one, of each matrix. If there is not an inverse, say that the matrix is singular.

In Problems 2934, find the inverse, if there is one, of each matrix. If there is not an inverse, say that the matrix is singular.

In Problems 2934, find the inverse, if there is one, of each matrix. If there is not an inverse, say that the matrix is singular.

In Problems 2934, find the inverse, if there is one, of each matrix. If there is not an inverse, say that the matrix is singular.

In Problems 2934, find the inverse, if there is one, of each matrix. If there is not an inverse, say that the matrix is singular.

In Problems 3544, solve each system of equations using matrices. If the system has no solution, say that it is inconsistent.

In Problems 3544, solve each system of equations using matrices. If the system has no solution, say that it is inconsistent.

In Problems 3544, solve each system of equations using matrices. If the system has no solution, say that it is inconsistent.

In Problems 3544, solve each system of equations using matrices. If the system has no solution, say that it is inconsistent.

In Problems 3544, solve each system of equations using matrices. If the system has no solution, say that it is inconsistent.

In Problems 3544, solve each system of equations using matrices. If the system has no solution, say that it is inconsistent.

In Problems 3544, solve each system of equations using matrices. If the system has no solution, say that it is inconsistent.

In Problems 3544, solve each system of equations using matrices. If the system has no solution, say that it is inconsistent.

In Problems 3544, solve each system of equations using matrices. If the system has no solution, say that it is inconsistent.

In Problems 3544, solve each system of equations using matrices. If the system has no solution, say that it is inconsistent.

In Problems 4550, find the value of each determinant

In Problems 4550, find the value of each determinant

In Problems 4550, find the value of each determinant

In Problems 4550, find the value of each determinant

In Problems 4550, find the value of each determinant

In Problems 4550, find the value of each determinant

In Problems 5156, use Cramers Rule, if applicable, to solve each system

In Problems 5156, use Cramers Rule, if applicable, to solve each system

In Problems 5156, use Cramers Rule, if applicable, to solve each system

In Problems 5156, use Cramers Rule, if applicable, to solve each system

In Problems 5156, use Cramers Rule, if applicable, to solve each system

In Problems 5156, use Cramers Rule, if applicable, to solve each system

In Problems 57 and 58, use properties of determinants to find the value of each determinant if it is known that . ` x y a b ` = 8

In Problems 57 and 58, use properties of determinants to find the value of each determinant if it is known that . ` x y a b ` = 9

In Problems 5968, write the partial fraction decomposition of each rational expression.

In Problems 5968, write the partial fraction decomposition of each rational expression.

In Problems 5968, write the partial fraction decomposition of each rational expression.

In Problems 5968, write the partial fraction decomposition of each rational expression.

In Problems 5968, write the partial fraction decomposition of each rational expression.

In Problems 5968, write the partial fraction decomposition of each rational expression.

In Problems 5968, write the partial fraction decomposition of each rational expression.

In Problems 5968, write the partial fraction decomposition of each rational expression.

In Problems 5968, write the partial fraction decomposition of each rational expression.

In Problems 5968, write the partial fraction decomposition of each rational expression.

In Problems 6978, solve each system of equations

In Problems 6978, solve each system of equations

In Problems 6978, solve each system of equations

In Problems 6978, solve each system of equations

In Problems 6978, solve each system of equations

In Problems 6978, solve each system of equations

In Problems 6978, solve each system of equations

In Problems 6978, solve each system of equations

In Problems 6978, solve each system of equations

In Problems 6978, solve each system of equations

In Problems 7982 graph each inequality

In Problems 7982 graph each inequality

In Problems 7982 graph each inequality

In Problems 7982 graph each inequality

In Problems 8388, graph each system of inequalities. Tell whether the graph is bounded or unbounded, and label the corner points.

In Problems 8388, graph each system of inequalities. Tell whether the graph is bounded or unbounded, and label the corner points.

In Problems 8388, graph each system of inequalities. Tell whether the graph is bounded or unbounded, and label the corner points.

In Problems 8388, graph each system of inequalities. Tell whether the graph is bounded or unbounded, and label the corner points.

In Problems 8388, graph each system of inequalities. Tell whether the graph is bounded or unbounded, and label the corner points.

In Problems 8388, graph each system of inequalities. Tell whether the graph is bounded or unbounded, and label the corner points.

In Problems 8992, graph each system of inequalities.

In Problems 8992, graph each system of inequalities.

In Problems 8992, graph each system of inequalities.

In Problems 8992, graph each system of inequalities.

In Problems 9396, solve each linear programming problem

In Problems 9396, solve each linear programming problem

In Problems 9396, solve each linear programming problem

In Problems 9396, solve each linear programming problem

Find A so that the system of equations has infinitely many solutions.

Find A so that the system in Problem 97 is inconsistent.

Find the quadratic function that passes through the three points and

Find the general equation of the circle that passes through the three points and [Hint: The general equation of a circle is ]

A coffee distributor is blending a new coffee that will cost $6.90 per pound. It will consist of a blend of $6.00 per pound coffee and $9.00 per pound coffee. What amounts of each type of coffee should be mixed to achieve the desired blend? [Hint: Assume that the weight of the blended coffee is 100 pounds.

A 1000-acre farm in Illinois is used to grow corn and soybeans. The cost per acre for raising corn is $65, and the cost per acre for soybeans is $45. If $54,325 has been budgeted for costs and all the acreage is to be used, how many acres should be allocated for each crop?

A cookie company makes three kinds of cookies, oatmeal raisin, chocolate chip, and shortbread, packaged in small, medium, and large boxes. The small box contains 1 dozen oatmeal raisin and 1 dozen chocolate chip; the medium box has 2 dozen oatmeal raisin, 1 dozen chocolate chip, and 1 dozen shortbread; the large box contains 2 dozen oatmeal raisin, 2 dozen chocolate chip, and 3 dozen shortbread. If you require exactly 15 dozen oatmeal raisin, 10 dozen chocolate chip, and 11 dozen shortbread, how many of each size box should you buy?

A store that specializes in selling nuts has available 72 pounds (lb) of cashews and 120 lb of peanuts. These are to be mixed in 12-ounce (oz) packages as follows: a lower-priced package containing 8 oz of peanuts and 4 oz of cashews and a quality package containing 6 oz of peanuts and 6 oz of cashews. (a) Use x to denote the number of lower-priced packages and use y to denote the number of quality packages. Write a system of linear inequalities that describes the possible number of each kind of package. (b) Graph the system and label the corner points

On a recent trip to the Cuyabeno Wildlife Reserve in the Amazon region of Ecuador, Mike took a 100-kilometer trip by speedboat down the Aguarico River from Chiritza to the Flotel Orellana. As Mike watched the Amazon unfold, he wondered how fast the speedboat was going and how fast the current of the white-water Aguarico River was. Mike timed the trip downstream at 2.5 hours and the return trip at 3 hours. What were the two speeds?

On a flight between Midway Airport in Chicago and Ft. Lauderdale, Florida, a Boeing 737 jet maintains an airspeed of 475 miles per hour. If the trip from Chicago to Ft. Lauderdale takes 2 hours, 30 minutes and the return flight takes 2 hours, 50 minutes, what is the speed of the jet stream? (Assume that the speed of the jet stream remains constant at the various altitudes of the plane and that the plane flies with the jet stream one way and against it the other way.)

If Bruce and Bryce work together for 1 hour and 20 minutes, they will finish a certain job. If Bryce and Marty work together for 1 hour and 36 minutes, the same job can be finished. If Marty and Bruce work together, they can complete this job in 2 hours and 40 minutes. How long will it take each of them working alone to finish the job?

A factory manufactures two kinds of ceramic figurines: a dancing girl and a mermaid. Each requires three processes: molding, painting, and glazing.The daily labor available for molding is no more than 90 work-hours, labor available for painting does not exceed 120 work-hours, and labor available for glazing is no more than 60 work-hours. The dancing girl requires 3 work-hours for molding, 6 work-hours for painting, and 2 work-hours for glazing. The mermaid requires 3 work-hours for molding, 4 work-hours for painting, and 3 work-hours for glazing. If the profit on each figurine is $25 for dancing girls and $30 for mermaids, how many of each should be produced each day to maximize profit? If management decides to produce the number of each figurine that maximizes profit, determine which of these processes has work-hours assigned to it that are not used.

A factory produces gasoline engines and diesel engines. Each week the factory is obligated to deliver at least 20 gasoline engines and at least 15 diesel engines. Due to physical limitations, however, the factory cannot make more than 60 gasoline engines nor more than 40 diesel engines in any given week. Finally, to prevent layoffs, a total of at least 50 engines must be produced. If gasoline engines cost $450 each to produce and diesel engines cost $550 each to produce, how many of each should be produced per week to minimize the cost? What is the excess capacity of the factory; that is, how many of each kind of engine is being produced in excess of the number that the factory is obligated to deliver?

Describe four ways of solving a system of three linear equations containing three variables. Which method do you prefer? Why?