The sum of the perimeter of the rectangles is 40cm. the sum of their area is 46 cm^2. find the values of x and y. could you explain how to do the calculation?

So for this, we will be doing a system of equations, one representing the sum of their areas and the other representing the sum of their perimeters:

So with this, I will be using the elimination method. So firstly, subtract 22 on both sides of the second equation:

Next, subtract the second equation from the first equation and you should get . From here we can solve for y.

For this, just divide both sides by 7 and your first answer will be y = 4.

Now that we have the value of y, substitute it into either equation to solve for x as such:

In short, x = 5 and y = 4.