Quiz.
tentukan nilai
a² + b² - (a - b)² × 11 - 5
jika nilai a = hasil 6x + 7y
jika diketahui SPLDV
x - 4y = -8
2x + y = 11
dan jika nilai b = hasil 7x - 12y
jika diketahui SPLDV
x - 2y = - 5
3x + 4y = 5
tentukan nilai
a² + b² - (a - b)² × 11 - 5
jika nilai a = hasil 6x + 7y
jika diketahui SPLDV
x - 4y = -8
2x + y = 11
dan jika nilai b = hasil 7x - 12y
jika diketahui SPLDV
x - 2y = - 5
3x + 4y = 5
Verified answer
Penjelasan dengan langkah-langkah:
SPLDV DAN ALJABAR
a² + b² - (a-b)² × 11 - 5
menentukan nilai a dari penyelesaian SPLDV dalam soal
x-4y = -8
2x+y = 11
Metode substitusi
x -4y = -8 → x = -8+4y
2x + y = 11
2(-8+4y) + y = 11
-16+8y+y = 11
9y = 11+16
9y = 27 .....kedua ruas bagi 9
y = 3
x-4y = -8
x-4(3) = -8
x -12 = -8
x = -8 + 12
x = 4
Maka
a = 6x + 7y
a = 6(4) + 7(3)
a = 24+21
a = 45
Untuk Nilai b , kita menentukan pada penyelesaian SPLDV
x-2y = -5
3x + 4y = 5
Metode substitusi
x-2y = -5 → x = -5 + 2y
3x + 4y = 5
3(-5+2y) + 4y = 5
-15+6y + 4y = 5
10y = 5+15
10y = 20 ....kedua ruas bagi 10
y = 2
x - 2y = -5
x - 2(2) = -5
x -4 = -5
x = -5+4
x = -1
Maka nilai b
b = 7x - 12y
b = 7(-1) - 12(2)
b = -7 -24
b = -31
Nilai
a² + b² - ((a-b)² × 11) - 5
= 45² + (-31)² - ((45-(-31)²×11) - 5
= 2025 + 961 - ((76)²×11) - 5
= 2981 - ( 63536 )
= -60555
a² + b² - (a - b)² × 11 - 5 = ?
Eliminasi SPLDV pertama
x - 4y = -8 |×2| 2x - 8y = -16
2x + y = 11 |×1 | 2x + y = 11
_________-
-9y = -27
y = 3
Substitusi y
x - 4y = -8
x - 4(3) = -8
x = -8 + 12
x = 4
Cari nilai a
a = 6x + 7y
a = 6(4) + 7(3)
a = 24 + 21
a = 45
Eliminasi SPLDV kedua
x - 2y = -5 |×2| 2x - 4y = -10
3x + 4y = 5 |×1 | 3x + 4y = 5
__________+
5x = -5
x = -1
Substitusi x
x - 2y = -5
-1 - 2y = -5
5 - 1 = 2y
y = 4/2
y = 2
Cari nilai b
b = 7x - 12y
b = 7(-1) - 12(2)
b = -7 - 24
b = -31
a² + b² - (a - b)² × 11 - 5
= (45)² + (-31)² - (45 - (-31))² × 11 - 5
= 2.025 + 961 - ((45 + 31)² × 11) - 5
= 2.025 + 961 - (76² × 11) - 5
= 2.986 - (5.776 × 11) - 5
= 2.986 - 63.536 - 5
= -60.555
Maka hasilnya adalah -60.555.