The perimeter of a fence is 140 feet. The sum of three times the length and two times the width is 180 feet. What are the length
and width of the fence?
1 answer:
Answer:
The length of the fence is
The width of the fence is
Step-by-step explanation:
Let
x-----> the length of the fence
y----> the width of the fence
we know that
The perimeter of the fence is equal to
so
------> equation A
-----> equation B
Using a graphing tool----> solve the system of equations
Remember that the intersection point both graphs is the solution of the system of equations
The solution is the point
see the attached figure
therefore
The length of the fence is
The width of the fence is
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Sorry I am a little late...
a = -2
b = -9
Here is how to solve the problem.
First thing I did was multiply the first equation by -2 so that we can eliminate the the b. After you multiply it by -2, your new equation is -16a + 8b = -40.
You leave the second equation alone and all you do is combine like terms. So -16a+5a is -11. And you eliminate the b. Then you're going to do -40+62 which is 22. So it's -11a=22 and then you have to solve for a. What I did was I multiplied the whole thing by minus to turn the a positive. So then it's 11a=-22. Pretty easy, the final step is to simplify. -22/11 is -2. ;D
So there you have your first answer.
a = -2
Now we're going to use the first answer to help us find b.
For the second equation, all you're going to do is plug in that a.
5 (-2)-8b=62
-10 - 8b = 62
Now we move the -10 to the other side...
-8b = 62 + 10
-8b = 72
Multiply the whole thing by negative once again to turn the b positive.
Now we have 8b = -72
The final step is to simplify. -72/11 = -9
b = -9
Hope this makes sense! Also I had the same question on my test and I got it right. :)
a = -2
b = -9
Here is how to solve the problem.
First thing I did was multiply the first equation by -2 so that we can eliminate the the b. After you multiply it by -2, your new equation is -16a + 8b = -40.
You leave the second equation alone and all you do is combine like terms. So -16a+5a is -11. And you eliminate the b. Then you're going to do -40+62 which is 22. So it's -11a=22 and then you have to solve for a. What I did was I multiplied the whole thing by minus to turn the a positive. So then it's 11a=-22. Pretty easy, the final step is to simplify. -22/11 is -2. ;D
So there you have your first answer.
a = -2
Now we're going to use the first answer to help us find b.
For the second equation, all you're going to do is plug in that a.
5 (-2)-8b=62
-10 - 8b = 62
Now we move the -10 to the other side...
-8b = 62 + 10
-8b = 72
Multiply the whole thing by negative once again to turn the b positive.
Now we have 8b = -72
The final step is to simplify. -72/11 = -9
b = -9
Hope this makes sense! Also I had the same question on my test and I got it right. :)