A value that gives no solution is 10; A value that gives infinitely many solutions is 20.
Work Step by Step
Let z be the variable for our blank; Given the system of equations: 3x+2y=10 6x+4y=z We know that if we set z to 10, it will have no solutions. Since 3x+2y=10, 6x+4y=10 cannot be true. Additionally, we know that (equation 1)$\times$2 is: 6x+4y=20 Therefore, if we set z=20, the equations will be equivalent, and the system will have an infinite amount of solutions.