Section 10.1

1.

Solve the given system of equations. If the system has no solution, say that it is inconsistent. X - 2y + 3z = 11 2x + y + z= -3 - 3x + 2y - 2z = -4 Select the correct choice below and fill in any answer boxes within your choice. O A. The solution is x = and z = (Type integers or simplified fractions.) O B. There are infinitely many solutions. Using ordered triplets, they can be expressed as { ( x , y , z ) | x = ,y= Z any real number} (Simplify your answers. Type expressions using z as the variable as needed.) O C. There are infinitely many solutions. Using ordered triplets, they can be expressed as {(x,y,z) x = ,y any real number, z any real number} (Simplify your answer. Type an expression using y and z as the variables as needed.) O D. The system is inconsistent.Solve the system of equations. If the system has no solution, say that it is inconsistent. X - y - Z= 4 4x + 4y + Z= 5 10x + 6y = 0 Select the correct choice below and, if necessary, fill in any answer boxes within your choice. O A. The solution is x = y = and z = (Type integers or simplified fractions.) O B. There are infinitely many solutions. The solutions set is { (x,y,z) | x = V= z is any real number}. (Simplify your answers. Type expressions using z as the variable.) O C. There are infinitely many solutions. The solution set is {(x,y,z) | x= , y is any real number, z is any real number} (Simplify your answer. Type an expression using y and z as the variables.) O D. The system is inconsistent.Solve the system of equations. If the system has no solution, say that it is inconsistent. X - y - Z= 2 -x + 2y - 3z = -5 3x - y - 11z = ( Select the correct choice below and, if necessary, fill in any answer boxes within your choice. A. The solution is x = y= and z = .(Type integers or simplified fractions.) O B. There are infinitely many solutions. The solution set is {(x,y,z) | x = V= z is any real number} (Simplify your answers. Type expressions using z as the variable.) O C. There are infinitely many solutions. The solution set is {(x, y, z) x = y is any real number, z is any real number} (Simplify your answer. Type an expression using y and z as the variables.) O D. The system is inconsistent.A store sells cashews for $5.00 per pound and peanuts for $1 .00 per pound. The manager decides to mix 33 pounds of peanuts with some cashews and sell the mixture for $2.00 per pound. How many pounds of cashews should be mixed with the peanuts so that the mixture will produce the same revenue as selling the nuts separately\"? Select the correct choice below and, if necessary. fill in the answer box to complete your choice. '3' A- There should be pounds of cashews in the mixture. [Type an integer or a decimal.) {.1 B. There are no mixtures that satisfy the given conditions Find real numbers a, b, and c so that the graph of the function y = ax + bx + c contains the points (1,2), (-2,9), and (0,3). Select the correct choice below and fill in any answer boxes within your choice. O A. The solution is a = b= and c = . (Type integers or simplified fractions.) O B. There are infinitely many solutions. Using ordered triplets, they can be expressed as {(a,b,c) | a = ,b= c any real number} (Simplify your answers. Type expressions using c as the variable as needed.) O C. There are infinitely many solutions. Using ordered triplets, they can be expressed as (a,b,c) | a = b any real number, c any real number} (Simplify your answer. Type an expression using b and c as the variables as needed.) O D. There is no solution.A Broadway theater has 490 seats, divided into orchestra: main, and balcony seating. Orchestra seats sell for $160: main seats for $125: and balcony seats for $1 'l. If all the seats are sold, the gross revenue to the theater is $62550. If all the main and balcony seats are sold, but only half the orchestra seats are sold, the gross revenue is 553350. How many of each kind of seat are there\"? Select the correct choice below and, if necessary: fill in the answer box(esj to complete your choice. {it A. There are orchestra seats= main seats: and balcony seats. (Type integers or fractions.) There are infinitely many solutions. There are orchestra seats, main seats. and z balcony seats; where 2 can be any real number. (Type expressions using 2 as the variable. Use integers or fractions for any numbers in the expressions} - There are infinitely many solutions. There are orchestra seats, y main seats: and z balcony seats, where y and 2 can be any real number. (Type expression using y and 2 as the variables. Use integers or fractions for any numbers in the expression} There are no combinations of seats that fit the conditions. An expression that occurs in calculus is given. Factor the given expression completely. 2(3x - 4) . 3(2x + 1)3 + (3x - 4)2 - 3(2x + 1)2 - 2 Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. 2(3x - 4) . 3(2x + 1) + (3x - 4)