Give the solutions please

Solve the system by using elementary row operations on the equations. Follow the systematic elimination procedure. 7x1+14x2 = 14 5x1+7x2 = 3 Find the solution to the system of equations. D (Simplify your answer. Type an ordered pair.) 1.1 .16 Question Help V a Determine if the given system is consistent. Do not completely solve the system. 2x1 - 8x4 = 16 4x2 + 4x3 = 0 x3 + 8x4 = 5 -5x1 +3x2 +5x3 + x4 = 15 Choose the correct answer below. 0 A. The system is consistent. O B. The system is inconsistent. O C. It is impossible to determine whether the system is consistent. 1.1 .17 Question Help V a Do the three lines 3x1 -4x2 =2, 6x1 + 13x2 = - 59, and 3x1 - 17x2 = 61 have a common point of intersection? Explain. Choose the correct answer below. 0 A. The three lines have at least one common point of intersection. O B. The three lines do not have a common point of intersection. O C. There is not enough information to determine whether the three lines have a common point of intersection. 1.1 .18 Question Help V a Do the three planes x1 + 3x2 +x3 = 5, x2 x3 =1, and 2x1 + 8x2 = 9 have at least one common point of intersection? Explain. Choose the correct answer below. 0 A. The three planes have at least one common point of intersection. O B. The three planes do not have a common point of intersection. O C. There is not enough information to determine whether the three planes have a common point of intersection. 1.1.21 Question Help Determine the value(s) of h such that the matrix is the augmented matrix of a consistent linear system. 4 2h - 4 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The matrix is the augmented matrix of a consistent linear system if h # (Use a comma to separate answers as needed. Type an integer or a simplified fraction.) O B. The matrix is the augmented matrix of a consistent linear system if h = (Use a comma to separate answers as needed. Type an integer or a simplified fraction.) O C. The matrix is the augmented matrix of a consistent linear system for every value of h. O D. The matrix is not the augmented matrix of a consistent linear system for any value of h.1.1.22 Question Help Determine the value(s) of h such that the matrix is the augmented matrix of a consistent linear system. - 12 6 h 4 -2 - 1 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The matrix is the augmented matrix of a consistent linear system if h = (Use a comma to separate answers as needed. Type an integer or a simplified fraction.) O B. The matrix is the augmented matrix of a consistent linear system if h # (Use a comma to separate answers as needed. Type an integer or a simplified fraction.) O C. The matrix is the augmented matrix of a consistent linear system for every value of h. O D. The matrix is not the augmented matrix of a consistent linear system for any value of h.1.1.23 Question Help V 0 Indicate whether the statements given in parts (a) through (d) are true or false and justify the answer. a. Is the statement "Every elementary row operation is reversible" true or false? Explain. O A. False, because only interchanging is a reversible row operation. 0 B. False, because only scaling and interchanging are reversible row operations. 0 C. True, because interchanging can be reversed by scaling, and scaling can be reversed by replacement. 0 D. True, because replacement, interchanging, and scaling are all reversible. 1 .1-24 Question Help V a Indicate whether the statements given in parts (a) through (d) are true or false and justify the answer. a. Is the statement "Two matrices are row equivalent if they have the same number of rows" true or false? Explain. O A. False, because if two matrices are row equivalent it means that there exists a sequence of row operations that transforms one matrix to the other. 0 B. False, because if two matrices are row equivalent it means that they have the same number of row solutions. 0 0. True, because two matrices are row equivalent if they have the same number of rows and column equivalent if they have the same number of columns. 0 D. True, because two matrices that are row equivalent have the same number of solutions, which means that they have the same number of rows. 1 .1 .25 Question Helpv Q Find an equation involving 9, h, and k that makes this augmented matrix correspond to a consistent system. 1-4 79 012-1911 4 4 -9k What equation must be satised for the augmented matrix to correspond to a consistent system? Select the correct choice below and ll in the answer box to complete your choice. (Simplify your answer.) O A_ 4g+h-k= O B_ 4g-h+k= O C. 4ghk= O D_ 4g+h+k= 1.1.27 Question Help Suppose the system to the right is consistent for all possible values of f and g. What can you say about the coefficients c and d? Justify your answer. X1 + 23X2 = f cx1 + dx2 = g Select the correct answer below. O A. Since f and g are arbitrary and the system is consistent for all possible values of f and g, c= 0 and d = 1. Otherwise, the triangular form of the matrix will show that the system is inconsistent. O B. The row reduction of 1 23 f 23 to shows that d - 23c #0 since f and g are arbitrary. Otherwise, for some choices of f and g, the second c d g o d-23c g - of row could correspond to an equation of 0 = b, where b is nonzero. Thus, d # 23c. O C. Since f and g are arbitrary, c and d can be any value and the system will be consistent. O D. 23 The row reduction of 1 23 to shows that d - 23c = 0 since f and g are arbitrary. Otherwise, for some choices of f and g, the second c dg o d- 23c g - cf row could correspond to an equation of bx2 = 0 where b is nonzero. Thus, c = d = 0.1.1.29 Question Help Find the elementary row operation that transforms the first matrix into the second, and then find the reverse operation that transforms the second matrix into the first. 2 -3 - 6 -9 - 5 - 4 8 6 5 8 6 5 9 . 5 - 4 2 -3 -6 Find the elementary row operation that transforms the first matrix into the second. Choose the correct answer below. O A. Interchange row 1 and row 3. O B. Multiply row 1 by O C. Interchange row 2 and row 3. O D. Multiply row 1 by and add the result to row 3.1.1.3 Question Help Find the point (X1,X2 ) that lies on the line x1 + 2x2 =5 and on the line x1 - X2 = - 1. See the figure. X2 X1 The point (X1,X2 ) that lies on the line x1 + 2x2 =5 and on the line X1 - X2 = - 1 is (Simplify your answer. Type an ordered pair.)1.1.31 Question Help Find the elementary row operation that transforms the first matrix into the second, and then find the reverse row operation that transforms the second matrix into the first. - 4 2 0 - 4 2 0 0 5 - 3 6 0 5 - 3 6 2 - 2 2 -6 0 6 -2 - 6 Find the elementary row operation that transforms the first matrix into the second. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. Replace row 3 by its sum with times row 2. (Type an integer or a simplified fraction.) O B. Scale row 3 by (Type an integer or a simplified fraction.) O C. Interchange row 3 and row 2. O D. Replace row 3 by its sum with times row 1. (Type an integer or a simplified fraction.)1 .1 .7 Question Help V a The augmented matrix of a linear system has been reduced by row operations to the form shown. Continue the appropriate row operations and 1 6 3 _ 5 describe the solution set of the original system. 0 1 1 2 0 0 0 1 0 0 1 2 Select the correct choice below and, if necessary, ll in the answer boxes to complete your choice. O A- The solution set has exactly one element, , , (Type integers or simplied fractions.) O B. The solution set has inntely many elements. 0 C. The solution set is empty. 1.1.8 Question Help The augmented matrix of a linear system has been reduced by row operations to the form shown. Continue the appropriate row operations and 1 -460 describe the solution set of the original system. 0 150 0 0 40 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. The solution set contains one solution, (Type integers or simplified fractions.) O B. The solution set has infinitely many elements. O C. The solution set is empty.1.1.9 Question Help The augmented matrix of a linear system has been reduced by row operations to the form shown. Continue the appropriate row - 3 0 0 -4 operations and describe the solution set of the original system. 0 1 - 0 -6 0 0 - 2 4 0 0 0 1 3 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. The solution set contains one solution: (Type integers or simplified fractions.) O B. The solution set is empty. O C. The solution has infinitely many elements.1.1.11 Question Help Solve the system. X2 + 3X3 = 6 X1 + 4X2 + 4X3 = 2 2x1 + 7X2 + 5X3 = 5 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. The unique solution of the system is (Type integers or simplified fractions.) O B. The system has infinitely many solutions. O C. The system has no solution.1.1.12 Question Help Solve the system. X 1 4X2 + 2X3 = -7 -2x1 + 10X2 - 10X3 = 21 -2X1 + 16X2 - 28x3 = 57 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. The unique solution of the system is ( (Type integers or simplified fractions.) O B. The system has infinitely many solutions. O C. The system has no solutions.1.1.13 Question Help Solve the system. X 1 - 3X3 = 13 2x1 + 2X2 + 9X3 = - 9 X2 + 4X3 = -7 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. The unique solution of the system is (Type integers or simplified fractions.) O B. The system has infinitely many solutions. O C. The system has no solution.1.1 .15 Question Help V a Determine if the given system is consistent. Do not completely solve the system. 3x1 + 9x3 = 12 x2 - 2x4 = 2 5x2 + 9x3 + x4 = 5 9x1 + 8x4 = - 4 Choose the correct answer below. 0 A. The system is consistent because the system can be reduced to a triangular form that indicates that no solutions exist. 0 B. The system is consistent because the system can be reduced to a triangular form that indicates that a solution exists. 0 C. The system is inconsistent because the system cannot be reduced to a triangularform. O D. The system is inconsistent because the system can be reduced to a triangular form that contains a contradiction