Consider two equations describing the relationship between three variables X, Y., and Yz: X = a + b Y), (1) X=c-d Y. (2) where a, b, c, and d, are positive, known constants (numbers). The objective is to find values of X, Y, and Y, for which both equations are satisfied and as well Y; = Y. a. How many unknown variables are there? Clearly identify them. How many equations are there? Clearly identify them. Note that there should be as many equations as unknown variables. When this is the case, a unique solution exists. (Try to convince yourself that having only (1) and (2) Page 3 of 5 makes it impossible to solve for the unknown variables, by equating X from (1) to X from (2) and trying to solve for Y, and Y.) b. Replace both sides of the third equation (which one is it?) using expressions (1) and (2) to solve for X c. After solving for X. find the values of Y, and Y, and verify whether the third equation is satisfied