1. How many solutions does each linear system have? Explain. a) b) F * ** 2. Solve each linear system in two-space. a) x+y=8 x-y=13 b) 3.5x-2.1y 14 1.5x-0.3y=8 c) [x, y]=[-12, -7]+s[8, -5] [x, y] [2, -1]+[3, -2] d) [x, y]=[16, 1]+s[5, 1] [x, y]=[7, 12]+t[7, 3] 3. Determine the number of solutions for each system without solving. a) 3x+12y=-27 4x+2y=34 b) 12x-21y=9 8x-14y=3 c) [x, y] = [1,6]+s[3, -2] [x, y] = [4,4]+[-6, 4] d) [x, y] [-17,-7]+[8,-3] 8x-3y=11 e) -6x+45y=33 10x-75y=-55 f) [x, y]=[11, 12]+s[2,7] [x, y] [2, 3]+t[1, 4] 4. Determine if the parallel lines in each pair are distinct or coincident. a) [x, y, z]=[5, 1, 3]+s[2, 1, 7] [x, y, z]=[2, 3, 9]+t[2, 1, 7] b) [x, y, z]-[4, 1, 0]+s[3, -5, 6] [x, y, z]=[13, 14, 18]+[-3, 5, -6] c) [x, y, z]=[5, 1, 3]+s[1, 4, -1] [x, y, z]=[3,-7, 5]+[2, -8,2] d) [x, y, z]=[4,8, 0]+s[7, 21, -14] [x, y, z]=[25, 55, 42]+[8, 24, 16] 5. Determine if the lines in each pair intersect. If so, find the coordinates of the point of intersection. a) [x, y, z]=[6, 5, 14]+s[1, 1, 3] [x, y, z] [11, 0, -17]+[4, -1, -6] b) [x, y, z]-[3, 2, 2]+s[1, 2,0] [x, y, z]=[1, 0, -1]+[0, 2, -3] c) [x, y, z]=[7, 0, 15]+s[2, 1, 5] [x, y, z]=[-7,-7, 20]+[2, 1, 5] d) [x, y, z] [8,-1, 8]+s[2, -3, 0] [x, y, z]=[1, 20, 0]+[1, -5,3] 6. Determine if the non-parallel lines in each pair are skew. a) [x, y, z]=[4, 7, -1]+s[-2, 1, 2] [x, y, z]=[1, 3, -1]+t[4, 1, 2] b) [x, y, z]=[6, 2, 1]+s[6, 18, 6] [x, y, z]=[7, 13, 1]+[6, 1, 2] c) [x, y, z]=[2,4,2]+s[2, 1, 5] [x, y, z]=[4, 3, 7]+[2, 1, 5] d) [x, y, z]=[-6, 12, 8]+s[2, 1, 5] [x, y, z]=[8,9,7]+t[2, 1, 5] e) [x, y, z]=[5, 4, 1]+s[6, 4, 2] [x, y, z]=[2, 3, 4]+t[1, 2, 3] f) [x, y, z]=[1, -1, 0]+s[2, 1, 3] [x, y, z]=[1, 2, 3]+[3, 2, 4]