Parallel_Platypus
New member
- Joined
- Dec 9, 2013
- Messages
- 8
When working on a problem in Geometry, I came across this simultaneous equation:
xy=24 and 2x+2y=20
After the help of Wolfram and some forum advice, I found the answer, it is either 4 or 6.
This is how:
Make x the subject of the first equation: x=24/y
Substitute into 2:
2(24/y)+2y=20
Expand= 48/y+2y=20
Multiply by y:
48+2y^2=20y
(I used Wolfram after this)
Move to the left side:
48/y+2y-20y=0
Factorise:
2(y-4)(y-6)=0
get rid of 2:
(y-4)(y-6)=0
This was all logical to me, then it said to simply "split" the equation and solve each bracket:
y-4=0
y=4 and
y-6=0
y=6
These answers are correct, but I am curious as to why the equation was split, how it is done, and how to know when it should be done. Thankyou!
xy=24 and 2x+2y=20
After the help of Wolfram and some forum advice, I found the answer, it is either 4 or 6.
This is how:
Make x the subject of the first equation: x=24/y
Substitute into 2:
2(24/y)+2y=20
Expand= 48/y+2y=20
Multiply by y:
48+2y^2=20y
(I used Wolfram after this)
Move to the left side:
48/y+2y-20y=0
Factorise:
2(y-4)(y-6)=0
get rid of 2:
(y-4)(y-6)=0
This was all logical to me, then it said to simply "split" the equation and solve each bracket:
y-4=0
y=4 and
y-6=0
y=6
These answers are correct, but I am curious as to why the equation was split, how it is done, and how to know when it should be done. Thankyou!