Solve the system. State whether the system is inconsistent or has infinitely many solutions. If the system has infinitely many solutions, write the solution set with y arbitrary. 5x - 6y = 1 10x + 12y = - 2 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. There is one solution. The solution set is (Simplify your answer. Type an ordered pair.) O B. The system has infinitely many solutions. The solution set is (Simplify your answer. Type an ordered pair. Type an expression using y as the variable.) O C. The solution is the empty set.point(s ) possible Solve the following nonlinear system of equations analytically. 3x2 + 2y2 = 20 X - y= -4 . . . Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Simplify your answer.) O A. The solution set is (Type an ordered pair. Use a comma to separate answers as needed.) O B. There are infinitely many solutions. The solution set is { ( ,y)}, where y is any real number. O C. The solution set is O.Three students buy lunch in the cafeteria. One student buys 5 hamburgers, 5 orders of fries, and 1 soda for $22. Another student buys 1 hamburger, 1 order of fries, and 1 soda for $4. The third student buys 1 hamburger and 1 order of fries for $4. If possible, find the cost of each item. Interpret the results. ... Select the correct choice below and, if necessary, fill in any answer boxes within your choice. O A. The cost of a hamburger is $. The cost of an order of fries is $ . The cost of a soda is $ (Round to the nearest cent as needed.) O B. It is not possible to determine the cost of each item because the system has infinitely many solutions. The students each have a differently-priced prepaid meal plan. O C. It is not possible to determine the cost of each item because the system has no solution. One of the students was charged incorrectlyUse the specified row transformation to change the given 19 2 matrix. -6 7 -1 6RX + R2 4 7 0 What is the transformed matrix? 1 9 2 4 7 0The following augmented matrix is in row echelon form and represents a linear system. Use back-substitution to solve the system if possible. 12 0 2 0 0 What is the solution to the linear system? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The solution set is { } (Simplify your answer. Type an ordered triple.) O B. There are infinitely many solutions. The solution set is {x,,} (Type an ordered triple. Type an expression using x as the variable.) O C. There is no solution.The matrix associated with the solution to a system of linear equations in x, y, and z is given. Write the solution to the system, if it exists. 103 2 0 18 -4 0 0 0 6 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. X= y = Z = (Type an exact answer in simplified form. If there are infinitely many solutions, type an expression involving z for each coordinate where z represents all real numbers.) O B. There is no solution