Solve for x and y : 5/x+1 - 2/y-1 = 1/2, 10/x+1 + 2/y-1 = 5/2 .
Answers
2x + 3y = 23
5x - 20 = 8y
We have to find the value of x and y using Substitution method (means my putting values).
2x + 3y = 23
2x = 23 - 3y
x = \dfrac{23\:-\:3y}{2}
2
23−3y
__(1)
5x - 20 = 8y __(2)
Put value of equation (1) in equation (2) :
5 (\dfrac{23\:-\:3y}{2})(
2
23−3y
) - 20 = 8y
\dfrac{115\:-\:15y}{2}
2
115−15y
- \dfrac{20}{1}
1
20
= 8y
\dfrac{115\:-\:15y\:-40}{2}
2
115−15y−40
= 8y
115 - 15y - 40 = 2(8y)
75 - 15y = 16y
75 = 16y + 15y
75 = 31y
31y = 75
y = \dfrac{75}{31}
31
75
__(3)
Put value of equation (3) in equation (2) :
5x - 20 = (8) (\dfrac{75}{31})(
31
75
)
5x - 20 = \dfrac{600}{31}
31
600
5x = \dfrac{600}{31}
31
600
+ 20
5x = \dfrac{600\:+\:620}{31}
31
600+620
5x = \dfrac{1220}{31}
31
1220
x = \dfrac{1220}{31\:\times\:5}
31×5
1220
x = \dfrac{244}{31}
31
244