MATH SOLVE

9 months ago

Q:
# 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 β y = 37. Which is the password?

Accepted Solution

A:

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 β 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