Himpunan penyelesaian dari sistem persamaan : [tex] 2^{x-1} + 3^{y+1} = 11 \\ 2^{x+2} -3^{y-1} =15 [/tex] adalah?

Bab Eksponensial
Matematika SMA Kelas X

x = a
y = b

2ᵃ = p
3ᵇ = q

2ᵃ⁻¹ + 3ᵇ⁺¹ = 11
2ᵃ . 2⁻¹ + 3ᵇ . 3¹ = 11
p . 1/2 + q . 3 = 11
p/2 + 3q = 11 → dikali 8 → 4p + 24q = 88

2ᵃ⁺² - 3ᵇ⁻¹ = 15
2ᵃ . 2² - 3ᵇ . 3⁻¹ = 15
p . 4 - q . 1/3 = 15
4p - q/3 = 15

******************************
4p + 24q = 88
4p - q/3 = 15
---------------------- -
   24q + q/3 = 73

********* dikali 3 *********
   
   72q + q = 219
   73q = 219
   q = 219/73
   q = 3

4p + 24q = 88
4p + 24 . 3 = 88
4p + 72 = 88
4p = 88 - 72
p = 16/4
p = 4

***************************

2ᵃ = p
2ᵃ = 4
2ᵃ = 2²
a = 2

3ᵇ = q
3ᵇ = 3
3ᵇ = 3¹
b = 1

x = a = 2
y = b = 1

HP = { (2, 1) }