The perimeter of a rectangle of two numbers. The sum of the numbers is 163, and their difference is 33. Write two equations that would be used to solve the system
x + y = 163
x - y = 33
To find the perimeter of a rectangle, we need to know the lengths of its sides. Let's assume the lengths of the sides are x and y.
We are given two pieces of information:
1. The sum of the numbers is 163: x + y = 163
2. The difference between the numbers is 33: x - y = 33
To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution.
From equation 2 (x - y = 33), we can isolate x by adding y on both sides:
x = y + 33
Now, substitute this value of x into equation 1 (x + y =163):
(y + 33) + y = 163
Simplify the equation:
2y + 33 = 163
Now, isolate y by subtracting 33 from both sides:
2y = 163 - 33
2y = 130
Finally, solve for y by dividing both sides by 2:
y = 130/2
y = 65
Now that we have the value of y, we can substitute it back into any of the original equations to solve for x. Let's use equation 1:
x + y = 163
x + 65 = 163
x = 163 - 65
x = 98
Therefore, the two numbers are x = 98 and y = 65.
In conclusion, the two equations we used to solve the system are:
1. x + y = 163
2. x - y = 33