Consider now the equation: 3) Prove that for any integer value of z, there are integer solutions for z and y. 4) Parameterize the set of integer solutions (x, y, z) in terms of an integer z and an integer parameter k. Note, because the above equation represents a plane in 3-D space, the solutions are two dimensional, and thus require two parameters (in this case, z and k). 5) Are you confident that your parameterization captures all integer solutions (x, y, z)? Why? Now consider the system of equations: 7x + 3y + 5z 1. 6) Are there any integer solutions (,y, 2) that satisfy both these equations simultaneously? The intersection of two planes is a line, so give a 1-D integer parameterization of the integer solutions to this system. Consider now the equation: 3) Prove that for any integer value of z, there are integer solutions for z and y. 4) Parameterize the set of integer solutions (x, y, z) in terms of an integer z and an integer parameter k. Note, because the above equation represents a plane in 3-D space, the solutions are two dimensional, and thus require two parameters (in this case, z and k). 5) Are you confident that your parameterization captures all integer solutions (x, y, z)? Why? Now consider the system of equations: 7x + 3y + 5z 1. 6) Are there any integer solutions (,y, 2) that satisfy both these equations simultaneously? The intersection of two planes is a line, so give a 1-D integer parameterization of the integer solutions to this system