Question

the perimeter of a rectangle is 14 feet the length is 1 inch longer than the width.Write a system of linear equations and solve the resulting system. let x be the length and y be the width.

2x+2y=?

x=y+?

what is the length?
what is the width?

Answer 1

do it all in inches to make it easier so 14 ft is 168 inches.
2x+2y = 168
x=y+1
you are going to use both these equations and substitute between them.
we want to get down to only 1 variable so we are going to substitute one equation for the other like below.
2(y+1)+2y=168
Now distribute your two and then get all your y's on one side.
2y+2+2y=168
4y+2=168
4y=168-2
4y=166
y=166/4
y=41.5
Now take this back to the original problem and plug it in
2x+2(41.5)=168 now solve for x (which should be 1 more than 41.5)
2x+83=168
2x=85
x=85/2
x=42.5
but we could have just added 1 to y since we had the equation (x=y+1)