The wifi password of an Institute has 4 digits. When a student requests it, the following instruction is given: the first 2 digits correspond to a number x, and the last 2 to a number y, which satisfy that y + 2x = 63 and 3x − y = 37. Which is the password?

Let's solve the system of equations using the given information: 1. y + 2x = 63 2. 3x - y = 37 We have a system of two linear equations with two variables, x and y. We can solve for x and y using various methods, such as substitution or elimination. Let's use the elimination method here. Let's start by multiplying the second equation by 2 to make the coefficients of y in both equations equal: 2 * (3x - y) = 2 * 37 6x - 2y = 74 Now we have two equations with equal coefficients for y: 1. y + 2x = 63 2. 6x - 2y = 74 Let's add the first equation to the second equation to eliminate y: (y + 2x) + (6x - 2y) = 63 + 74 8x = 137 Now we can solve for x: x = 137 / 8 x = 17.125 However, since the first two digits of the WiFi password need to be integers, we can round down to the nearest integer: x ≈ 17 Now that we have the value of x, we can substitute it into one of the original equations to solve for y. Let's use the first equation: y + 2x = 63 y + 2 * 17 = 63 y + 34 = 63 y = 63 - 34 y = 29 So, the values of x and y that satisfy the given conditions are x = 17 and y = 29. The WiFi password consists of these two numbers: Password: xy = 1729