F.3-Linear Equations in Two Unknown

1.)A two-digit no.is four times the sum of its two digits.If we exchange the positions of the two digits and add 9 to the new no., the result becomes twice of the original no.Find the original no.
Let the number be (10a+b)
10a+b=(a+b)*4----------1
(10b+a)+9=2(10a+b)---------2
From 1,
10a+b=4a+4b
3b=6a
b=2a-----------3
Sub 3 into 2
10(2a)+a+9=2(10a+2a)
21a+9=20a+4a
3a=9
a=3 , b=2(3)=6
The number is 10(3)+6=36

2.)Alex and Billy are running on a circlar track of length 210m. They start running from the same position and Alex runs faster. If they run in the same direction, Alex will lead Billy a round after 1 minute. If they run in the opposite directions, they will meet after 20 seconds.Find their speeds.
Let the speed of Alex and Billy be u ms^-1 and v ms^-1 respectively
If they run in the same direction, Alex will lead Billy a round after 1 minute.
u(60)-v(60)=210-----------1
If they run in the opposite directions, they will meet after 20 seconds
u(20)+v(20)=210-----------2
From 1,
u=(2v+7)/2----------3
Sub 3 into 2
20[(2v+7)/2]+20v=210
10(2v+7)+20v=210
40v=140
v=3.5 , u=(2*3.5+7)/2=7
Therefore, the speed of Alex and Billy are 7 ms^-1 and 3.5 ms^-1 respectively

1.)A two-digit no.is four times the sum of its two digits.If we exchange the positions of the two digits and add 9 to the new no., the result becomes twice of the original no.Find the original no.


Let x be the ten digit no. y be the digit
xy = 4(x+y) …(1)
10y+x+9 = 2(10x+y) …(2)