SOLUTION: A rectangle has a perimeter P of 14 feet, and twice its length l is equal to 1 less than 4 times its width w. Write and solve a system of linear equations to find the length and th

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons  -> Linear Equations Lesson -> SOLUTION: A rectangle has a perimeter P of 14 feet, and twice its length l is equal to 1 less than 4 times its width w. Write and solve a system of linear equations to find the length and th      Log On


   

Question 850538: A rectangle has a perimeter P of 14 feet, and twice its length l is equal to 1 less than 4 times its width w. Write and solve a system of linear equations to find the length and the width of the rectangle.
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Given: Rectangle, perimeter P;
x is length
y is width
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x=-1+4y,
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UNKNOWNS: x and y.

IMPORTANT FACT
Perimeter for a rectangle, 2L+2W.

The current exercise in this solution uses x instead of L and y instead of W.
We are given P already.

highlight%282x%2B2y=P%29
and highlight%28x=4y-1%29.
Solve for x and y. Substitution would be a good way.
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2x%2B2y=2%284y-1%29%2B2y=P
8y-2%2B2y=P
10y-2=P
10y=P%2B2
highlight%28y=%28P%2B2%29%2F10%29
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Use the formula for y to make and simplify the formula for x.
x=4%28substituteHere%29-1
x=4%28%28P%2B2%29%2F10%29-1
That might be good as is, or...
%282%2F5%29%28P%2B2%29-1
%282%2F5%29%28P%2B2%29-5%2F5
%282%28P%2B2%29-5%29%2F5
%282P%2B4-5%29%2F5
x=highlight%28highlight%28%282P-1%29%2F5%29%29----Yes, this form is better.
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SUMMARY: Length, highlight%28x=%282P-1%29%2F5%29, and width, highlight%28y=%28P%2B2%29%2F10%29