Answer:
First solve for x
then substitute
Step-by-step explanation:
![\frac{x+3}{3}= \frac{y+2}{2}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%2B3%7D%7B3%7D%3D%20%5Cfrac%7By%2B2%7D%7B2%7D)
![6(\frac{x+3}{3}=\frac{y+2}{2})](https://tex.z-dn.net/?f=6%28%5Cfrac%7Bx%2B3%7D%7B3%7D%3D%5Cfrac%7By%2B2%7D%7B2%7D%29)
2x + 6 = 3y + 6
2x = 3y
![x = \frac{3y}{2}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B3y%7D%7B2%7D)
If
then
=
![x = \frac{3y}{2} /3 = \frac{y}3}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B3y%7D%7B2%7D%20%2F3%20%3D%20%5Cfrac%7By%7D3%7D)
Let the width of room be =x mtrs
Then the length is x+2 mtrs
As Perimeter = 2(l+b) = 2(x+x+2)
16 = 2 ( 2x+2)
16/2 = 2x +2
8=2x+2
2x= 8-2 = 6
x = 6/2 =3 mtrs
Therefore width of the room is 3 mtrs
Remark
This may be a little confusing, but because they are travelling in opposite directions, the distances add when you want to get how far apart they are.
d1 + d2 = 1541
Equation
Let the time this happens = t
d1 = 323*t
d2 = 347*t
323*t + 347*t = 1541 Combine like terms on the left.
670t = 1541 Divide by 670
t = 1541/670
t = 2.3 hours pass before the distance of 1541 miles are between the two planes. You might need the answer to be 2 hours 18 minutes.
Answer:
<h2>(-10, 2, 6)</h2>
Step-by-step explanation:
![\left\{\begin{array}{ccc}x+3y+2z=8&(1)\\3x+y+3z=-10&(2)\\-2x-2y-z=10&(3)\end{array}\right\qquad\text{subtract both sides of the equations (1) from (2)}\\\\\underline{-\left\{\begin{array}{ccc}3x+y+3z=-10\\x+3y+2z=8\end{array}\right }\\.\qquad2x-2y+z=-18\qquad(4)\qquad\text{add both sides of the equations (3) and (4)}\\\\\underline{+\left\{\begin{array}{ccc}-2x-2y-z=10\\2x-2y+z=-18\end{array}\right}\\.\qquad-4y=-8\qquad\text{divide both sides by (-4)}\\.\qquad\qquad y=2\qquad\text{put the value of y to (1) and (3)}](https://tex.z-dn.net/?f=%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bccc%7Dx%2B3y%2B2z%3D8%26%281%29%5C%5C3x%2By%2B3z%3D-10%26%282%29%5C%5C-2x-2y-z%3D10%26%283%29%5Cend%7Barray%7D%5Cright%5Cqquad%5Ctext%7Bsubtract%20both%20sides%20of%20the%20equations%20%281%29%20from%20%282%29%7D%5C%5C%5C%5C%5Cunderline%7B-%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bccc%7D3x%2By%2B3z%3D-10%5C%5Cx%2B3y%2B2z%3D8%5Cend%7Barray%7D%5Cright%20%7D%5C%5C.%5Cqquad2x-2y%2Bz%3D-18%5Cqquad%284%29%5Cqquad%5Ctext%7Badd%20both%20sides%20of%20the%20equations%20%283%29%20and%20%284%29%7D%5C%5C%5C%5C%5Cunderline%7B%2B%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bccc%7D-2x-2y-z%3D10%5C%5C2x-2y%2Bz%3D-18%5Cend%7Barray%7D%5Cright%7D%5C%5C.%5Cqquad-4y%3D-8%5Cqquad%5Ctext%7Bdivide%20both%20sides%20by%20%28-4%29%7D%5C%5C.%5Cqquad%5Cqquad%20y%3D2%5Cqquad%5Ctext%7Bput%20the%20value%20of%20y%20to%20%281%29%20and%20%283%29%7D)
![\left\{\begin{array}{ccc}x+3(2)+2z=8\\-2x-2(2)-z=10\end{array}\right\\\left\{\begin{array}{ccc}x+6+2z=8&\text{subtract 6 from both sides}\\-2x-4-z=10&\text{add 4 to both sides}\end{array}\right\\\left\{\begin{array}{ccc}x+2z=2&\text{multiply both sides by 2}\\-2x-z=14\end{array}\right\\\underline{+\left\{\begin{array}{ccc}2x+4z=4\\-2x-z=14\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad3z=18\qquad\text{divide both sides by 3}\\.\qquad\qquad z=6\qquad\text{put the value of z to the first equation}](https://tex.z-dn.net/?f=%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bccc%7Dx%2B3%282%29%2B2z%3D8%5C%5C-2x-2%282%29-z%3D10%5Cend%7Barray%7D%5Cright%5C%5C%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bccc%7Dx%2B6%2B2z%3D8%26%5Ctext%7Bsubtract%206%20from%20both%20sides%7D%5C%5C-2x-4-z%3D10%26%5Ctext%7Badd%204%20to%20both%20sides%7D%5Cend%7Barray%7D%5Cright%5C%5C%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bccc%7Dx%2B2z%3D2%26%5Ctext%7Bmultiply%20both%20sides%20by%202%7D%5C%5C-2x-z%3D14%5Cend%7Barray%7D%5Cright%5C%5C%5Cunderline%7B%2B%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bccc%7D2x%2B4z%3D4%5C%5C-2x-z%3D14%5Cend%7Barray%7D%5Cright%7D%5Cqquad%5Ctext%7Badd%20both%20sides%20of%20the%20equations%7D%5C%5C.%5Cqquad%5Cqquad3z%3D18%5Cqquad%5Ctext%7Bdivide%20both%20sides%20by%203%7D%5C%5C.%5Cqquad%5Cqquad%20z%3D6%5Cqquad%5Ctext%7Bput%20the%20value%20of%20z%20to%20the%20first%20equation%7D)
![x+2(6)=2\\x+12=2\qquad\text{subtract 10 from both sides}\\x=-10](https://tex.z-dn.net/?f=x%2B2%286%29%3D2%5C%5Cx%2B12%3D2%5Cqquad%5Ctext%7Bsubtract%2010%20from%20both%20sides%7D%5C%5Cx%3D-10)
Step-by-step explanation:
maybe you can try to measure each of the ways maybe and you can get the equation