SOLUTION: The perimeter of a rectangle is 48 inches. The width of the rectangle is 2 more than half the length. . Write a system of linear equations to model this . Name the method you

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: The perimeter of a rectangle is 48 inches. The width of the rectangle is 2 more than half the length. . Write a system of linear equations to model this . Name the method you       Log On


   

Question 253244: The perimeter of a rectangle is 48 inches. The width of the rectangle is 2 more than half the length.
. Write a system of linear equations to model this
. Name the method you would use to solve system you wrote above
. Use the method you stated above to solve the system for the length and width of the rectangle stated above
Answer by Greenfinch(383) About Me  (Show Source):
You can put this solution on YOUR website!
Call width X and length Y
Perimeter is 2X + 2Y = 48
Relation is X-2 = Y/2 or 2X - Y = 4
You can solve by elimination
Take Equation 2 from equation 1 and get 3Y = 44 (Y = 14 2/3)
Substitute in equation 1 and get X = (48 - 2x(14 2/3))2 = 9 1/3
Check in equation 2 X - 2 = 7 1/3 Y/2 = 7 1/3 CHECKS
you can solve by substitution
from equation 1 X = 24 - Y
so in equation 2 (24 - Y) - 2 = Y/2
22 = 3/2 Y
y = 2/3 x 22 = 14 2/3
Amazing, it works both ways !!