Diketahui:
[tex] {2}^{x} \: . \: {8}^{y} = {2}^{8} \\ \sqrt{ {3}^{x} } \: . \: {27}^{y} = 9[/tex]
Nilai dari 2x - 2y adalah....
[tex] {2}^{x} \: . \: {8}^{y} = {2}^{8} \\ \sqrt{ {3}^{x} } \: . \: {27}^{y} = 9[/tex]
Nilai dari 2x - 2y adalah....
Penjelasan dengan langkah-langkah:
[tex]{2}^{x} \: . \: {8}^{y} = {2}^{8} \\ \sqrt{ {3}^{x} } \: . \: {27}^{y} = 9 \\ \\ \\ {2}^{x} . {2}^{3y} = {2}^{8} \\ {\cancel2}^{ x + 3y} = {\cancel2}^{8} \\ x + 3y = 8 \\ \\ {3}^{ \frac{x}{2} } . {3}^{3y} = {3}^{2} \\ \cancel{3}^{ \frac{x}{2} + 3y } = {\cancel3}^{2} \\ \frac{x}{2} + 3y = 2 \: ....kedua \: ruas \: kalikan \: 2 \\ x + 6y = 4 \\ \\ [/tex]
Diperoleh persamaan
Ditanya :
Jawab :
SPLDV METODE ELEMINASI
x+3y = 8
x+6y = 4
-------------- -
-3y = 4
y = -4/3
Subtitusikan nilai y
x+3y = 8
x+3(-4/3) = 8
x - 4 = 8
x = 8+4
x = 12
Maka
2x - 2y
= 2(12) - 2(-4/3)
= 24 +8/3
= 72/3 + 8/3
= 80/3
= 26 2/3
= 26,666
≈ 26,667
Verified answer
Jawaban:
2x - 2y = 124/6
Penjelasan dengan langkah-langkah:
[tex] {2}^{x} \times {8}^{y} = {2}^{8} [/tex]
[tex] {2}^{x} \times {2}^{3.y} = {2}^{8} [/tex]
[tex] {2}^{x + 3y} = {2}^{8} [/tex]
x + 3y = 8
x = 8 - 3y .........pers 1
[tex] \sqrt{{3}^{x} } \times {27}^{y} = 9[/tex]
[tex] \sqrt{{3}^{x} } \times {3}^{3.y} = {3}^{2} [/tex]
[tex] {3}^{ \frac{x}{2} } \times {3}^{3y} = {3}^{2} [/tex]
[tex] {3}^{ \frac{x}{2} + 3y} = {3}^{2} [/tex]
[tex] \frac{x}{2} + 3y = 2......... pers 2[/tex]
✍✍
nilai y:
[tex] \frac{x}{2} + 3y = 2[/tex]
[tex] \frac{8 - 3y}{2} + 3y = 2[/tex]
[tex] \frac{8 - 3y}{2} + \frac{3y}{1} = 2[/tex]
[tex] \frac{8 - 3y}{2} + \frac{6y}{2} = 2[/tex]
[tex] \frac{8 + 3y}{2} = 2[/tex]
[tex] \frac{4 + 3y}{1} = 2[/tex]
4 + 3y = 2
3y = -2
y = -2/3
nilai x:
x + 3y = 8
[tex]x + {3}^{ - \frac{2}{3} } = 8[/tex]
[tex]x + ( - 2) = 8[/tex]
x = 8 + 2
x = 10
nilai dari 2x - 2y
= 2(10) - 2(-2/3)
= 20 + 4/6
= 120/6 + 4/6
= 124/6
(8+3y)/2 = 4+(3/2)y
8+3y = 4
3y = -4, y = -4/3