Solve the system:x + 6y = 17x - 3y = 8SMP VIII
1. Solve the system:x + 6y = 17x - 3y = 8SMP VIII
x=11
y=1
Penjelasan dengan langkah-langkah:
x + 6y = 17 .......... (1)
x - 3y = 8 ............(2)
Eliminasi kedua persamaan menghasilkan :
x + 6y = 17 .......... (1)
x - 3y = 8 ............(2)
________________ -
9 y = 9 , y = 1
Substitusi y = 1 ke Persamaan 2 menghasilkan :
x - 3 (1) = 8
x - 3 = 8
x = 11
Maka (x,y) = (11,1)
2. apa yang di maksud dengan pertandingan DOUBLE ELIMINATION SYSTEM?
prtndingan DES sama dgn sistem KO(gugur) adalah slah satu format turnamen yg mlibatkan sluruh psrta awal turnamen.
3. 4) Selesaikanlah system persamaan berikut. -x + 2y + 3z = 0; x – 4y-13z = 0; -3x + 5y + 4z = 0.
- x + 2y + 3z = 0
- x = - 2y - 3z
x = 2y + 3z.... (1)
x - 4y - 13z = 0
2y + 3z - 4y - 13z = 0
(2-4)y + (3 - 13)z = 0
- 2y - 10z = 0... (2)
- 3x + 5y + 4z = 0
- 3(2y + 3z) + 5y + 4z = 0
- 6y - 9z + 5y + 4z = 0
(-6 + 5)y - (9 - 4)z = 0
- y - 5z = 0... (3)
Eliminasi persamaan (2) dan (3) - 2y - 10z = 0I×-1I 2y + 10z = 0
- y - 5z = 0 I×-2I 2y + 10z = 0
--------------------------------------------
y = 0, z = 0, x = 0
4. what is the solution to this system of lunear equqtion use elimination 3x+ y=-14 -2x-y=9
Jawaban:
x = -5, y = 1
Penjelasan:
Materi : Matematika - Sistem Linear
Persamaan :
3x + y = -14
-2x - y = 9
Gunakan teknik eliminasi dan substitusi
kita eliminasi variabel y
3x + y = -14
-2x - y = 9 +
x = -5
Substitusikan x ke aalah satu variabel
-2x - y = 9
-2(-5) - y = 9
10 - y = 9
-y = 9-10
-y = -1
y = 1
TESTING VARIABLE
3x + y = -14
3(-5) + (1) = -14
-15 + 1 = -14
-14 = -14 (BENAR)
-2x - y = 9
-2(-5) - 1 = 9
10 - 1 = 9
9 = 9 (BENAR)
Jadi, nilai x dan y yang memenuhi persamaan diatas adalah (-5,1) atau x = -5 dan y = 1
Rujukan : Matematika SMP Kelas VIII KTSP 2006 (2008), Kemendikbud.
Selamat belajar ! Jangan takut untuk trial and error dalam belajar !
5. penjumlahan 16x - 5y + 4z dan x - 9z + 3y adalah
Jawab:
17x-2y-5z
Penjelasan dengan langkah-langkah:
(16x-5y+4z) + (x+3y-9z)
17x-2y-5z
Jawaban:
17x - 2y - 5z
Penjelasan dengan langkah-langkah:
(16x - 5y + 4z) + (x - 9z + 3y)
= 16x - 5y + 4z + x - 9z + 3y
nah sekarang agar lebih mudah yang variabelnya sama disejajarkan.
16x + x - 5y + 3y + 4z - 9z
kita hasilkan yang variabelnya sama
16x + x = 17x
-5y + 3y = -2y
4z - 9z = -5z
Jadi hasilnya adalah
17x - 2y - 5z
6. Solving systems by elimination
-3x - 3y = 12
-4x + 3y = -24
---------------------- +
-7x = -12
x = -12/(-7)
x = 12/7
-3x - 3y = 12 (× 4)
-4x + 3y = -24 (× 3)
-12x - 12y = 48
-12x + 9y = -72
---------------------- -
-21y = 120
y = 120/(-21)
y = -40/7
so HP = {12/7 , -40/7}
7. Determine the solving of system linear equation two variables by elimination 1.) 3x+4y-20=0 & 4x=3y+10 2.) 4x-5y=-12 & 2x+3y=13 3.) 3x-2y-12=0 & 4x-3y-7=0
1.) 3x+4y-20=0 & 4x=3y+10
3x+4y=20..........x3 9x+12y=60
4x-3y=10...........x4 16x-12y=40
25x=100
x=4
3x+4y=20..........x4 12x+16y=80
4x-3y=10...........x3 12x-9y=30
25y=50
y=2
2.) 4x-5y=-12 & 2x+3y=13
4x-5y=-12............x2 8x-10y=-24
2x+3y=13.............x4 8x+12y=52
-22y=-76
y=76/22
4x-5y=-12............x3 12x-15y=-36
2x+3y=13.............x5 10x+15y=65
22x=29
x=29/22
3.) 3x-2y-12=0 & 4x-3y-7=0
3x-2y=12 ...........x4 12x-8y=48
4x-3y=7 .............x3 12x-9y=21
y=27
3x-2y=12 ...........x3 9x-6y=36
4x-3y=7 .............x2 8x-6y=14
x=22
8. how do you solve 4x + y = 2 using elimination method
there's no other equation
9. hasil 10×-5y-6z dan -5×+2y+ 4z
Jawaban:
10x - 5y - 6z + (-5x) + 2y + 4z
= 10x - 5y - 6z - 5x + 2y + 4z
= 10x - 5x - 5y + 2y - 6z + 4z
= 5x - 3y - 2z
SEMOGA MEMBANTU!!
10. 2x-5y-z=83x+y+4z=10x-2y+3z=12
Semoga Membantu
Keterangan
A. Pindahkan variabel
B. Bagi kedua ruas persamaan
C. Penyelesaian akhir untuk X
11. Himpunan penyelesaian dari —x–5y–5z=2 4x–5y+4z=19 x+5y–z=–20
moga membantu
selamat belajarr
12. Jika x= 5y, y=4z dan x+y+2=100 maka
Jawaban:
humpunan penyelesaian x, y, z adalah {80, 16, 4}
Penjelasan dengan langkah-langkah:
x = 5y
y = 4z
subtitusi nilai y
x = 5(4z)
x = 20z
[tex]___________[/tex]
subtitusi nilai x dan y terhadap persamaan
x + y + z = 100
= 20z + 4z + z = 100
= 25z = 100
= z = [tex] \sf \frac{100}{25}[/tex]
= z = 4
[tex]___________[/tex]
subtitusi nilai z ke persamaan y
y = 4z
y = 4 × 4
y = 16
[tex]___________[/tex]
x = 5y
x = 5 × 16
x = 80
13. using the elimination method,solve each of the following pairs of simultaneous equations.[tex] \frac{x + 1}{y + 2} = \frac{3}{4} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \frac{x - 2}{y - 1} = \frac{3}{5} [/tex]
Jawaban:
[tex] \frac{x + 1}{y + 2} = \frac{3}{4} \\ 4(x + 1) = 3(y + 2) \\ 4x + 4 = 3y + 6 \\ 4x - 3y + 4 - 6 \\ 4x - 3y - 2[/tex]
[tex] \frac{x - 2}{y - 1} = \frac{3}{5} \\ 5(x - 2) = 3(y - 1) \\ 5x - 10 = 3y - 3 \\ 5x - 3y - 10 + 3 \\ 5x - 3y - 7[/tex]
14. 6 X 899 solve the sum by distributive property
Jawaban:
The form of the product of 6 × 37 using the distributive property is
= 6 × (30 + 7)
= (6 × 30) + (6 × 7)
= 180 + 42
= 222
Discussion
Using Distributive Properties in Multiplication
There are many quick and easy ways to solve a math problem, including:
1) Commutative (exchange)
What is meant by commutative is to change or reverse the position of a number. Commutative only applies to addition and multiplication because in the process of multiplication and addition, even though the place is exchanged or reversed, the result remains the same.
So, a × b is the same as b × a. Likewise a + b the result is the same as b + a.
2) Associative (grouping)
What is meant by associative is to group the counting process.
(a × b) × c = a x (b × c)
(a + b) + c = a + (b + c)
Just like commutative, associative also only applies to multiplication and addition.
3) Distributive (spread)
What is meant by distributive is to describe the form of multiplication into the form of addition or subtraction.
a × (b + c) = (a × b) + (a × c)
Well, on this occasion we will discuss problems related to the distributive property of multiplication.
Is known :
Multiply 6 × 37
Asked:
Solve with the distributive propertySolution:
First, the tens and ones in the number 37 are converted to addition form.
6 × (30 + 7)
Next, the tens and ones are multiplied by 6.
(6×30) + (6×7)
Then look for the results of the multiplication and the results are added up
= 180 + 42
=
= 6 × (30 + 7)
= (6 × 30) + (6 × 7)
= 180 + 42
= 222
Penjelasan dengan langkah-langkah:
sorry if wrong(•‿•)
15. find the solution to each of the following system of equations by elimination for example 2x+y=5 and 3x-2y=11
3x-2y=11 |×1
2x+y=5 |×2
⇒3x-2y =11}ini
4x+2y=10}dikurangkan ini
⇒-x=1 ⇔x=-1 dan y = 2x+y=5
2×-1+y =5
-2+y=5
y=7
16. 2x+5y-4z=-8 3x-5y-4z=-29 2x-6y-3z=-26 Tentukan nilai x+y+z (metode eliminasi)
jawaban terlampir ya.
17. 2x-5y-z=8;3x+y+4z=10;x-2y+3z=12.nilai x-y+z adalah
1. 2x - 5y - z = 8
2. 3x + y + 4z = 10
3. x - 2y + 3z = 12
Kita hilangkan z
Persamaan 1 dan 2
2x - 5y - z = 8 → x(4) →8x - 20y - 4z = 32
3x + y + 4x = 10 → x(1) → 3x + y + 4z = 10
_____________+
11x - 19y = 42 ........a)
Persamaan 1 dan 3
2x - 5y - z = 8 → x(3) → 6x - 15y - 3z = 24
x - 2y + 3z = 12 → x(1) → x - 2y + 3z = 12
_____________+
7x - 17y = 36 ......b)
11x - 19y = 42 → x(7) → 77x - 133y = 294
7x - 17y = 36 → x(11) → 77x - 187y = 396
_____________-
54y = -102
y = -102/54
y = -17/9
7x - 17(-17/9) = 36
7x + 289/9 = 36
7x = 324/9 - 289/9
7x = 35/9
x = 245/9
2x - 5y - z = 8
2(245/9) - 5(-17/9) - z = 8
490/9 + 85/9 - z = 8
575/9 - z = 8
-z = 72/9 - 575/9
-z = -503/9
z = 503/9
x - y + z = 245/9 - (-17/9) + 503/9
= 245/9 + 17/9 + 503/9
= 765/9
= 85
18. Hasil penjumlahan (2x + 3y - 8z) + (3x – 8y + 4z) adalah ... A. 5x - 5y - 4z C. 5x + 5y - 42 B. 5x - 5y + 4z D. 5x + 5y + 4z tolong bantu dong guys !
Jawaban:
A. 5x - 5y - 4z
Penjelasan dengan langkah-langkah:
(2x + 3y - 8z) + (3x - 8y + 4z)
= 2x + 3y - 8z + 3x - 8y + 4z
= 2x + 3x + 3y - 8y - 8z + 4z
= 5x - 5y - 4z
19. - 3x + y = 5 -6x + 5y = 20 . Elimination method ya
Jawab:
x = -5/9 dan y = 10/3
Penjelasan dengan langkah-langkah:
(-3x + y) * 2 = 5 * 2
-6x + 2y = 10 (a)
-6x + 5y = 20 (b)
Sekarang, b kurang a menjadi
(-6x - (-6x)) + (5y - 2y) = 20 - 10
3y = 10
y = 10/3
(-3x + y) * 5 = 5 * 5
-15x + 5y =25 (c)
-6x + 5y = 20 (b)
Sekarang, c kurang b
(-15x - (-6x)) + (5y - 5y) = 25 - 20
-9x = 5
x = -5/9
20. Q5. Solve the equation -4(10 + 3x) - (x + 8) = -9
Jawab:
x = -3
Penjelasan dengan langkah-langkah:
-4(10 + 3x) - (x + 8) = -9
[-4.10 + (-4)(3x)] - [x + 8] = -9
[-40 - 12x] - x - 8 = -9
-40 - 8 - 12x - x = -9
-48 - 13x = -9
-48 + 9 = 13x
-39 = 13x
x = -39/13
x = -3
___
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