berapa nila x yang memenuhi 1/x + 1/y=10 dan 5/x -2/y=26

Bab Persamaan Linear
Matematika SMP Kelas VIII

1/x = p
1/y = q

p + q = 10 → dikali 2 menjadi 2p + 2q = 20

5p - 2q = 26
2p + 2q = 20
------------------- + 
        7p = 46
          p = 46/7

p + q = 10
46/7 + q = 10
q = 70/7 - 46/7
q = 24/7

1/x = p
1/x = 46/7
x = 7/46

1/y = q
1/y = 24/7
y = 7/24

HP = { (7/46, 7/24) }

y+x=10xy
x-10xy=-y
x(1-10y)=-y
x=-y/(1-10y)

5y-2x=26xy
-2x-26xy=-5y
x(-2-26y)=-5y
x=-5y/(-2-26y)

-y/(1-10y)=-5y/(-2-26y)
2y+26y^2=-5y+50y^2
0=-7y+24y^2
0=y(-7+24y)

y=7/24


1/x+1/(7/24)=10
1/x= 10-24/7
1/x = 46/7

X=7/46