tentukan nilai x dan y dari 1. x+2y = 13 x-4y= 17 2. 3x+5y= -7 4x+7y= -10 3. 0,1x+0,3y-2,8=0 0,4x-0,2y+1,2=0

Mapel : Matematika
Kelas : VIII SMP
Bab : SPLDV

Pembahasan :
1)

x + 2y = 13
x - 4y = 17
—————— (-)
6y = -4
y = -2/3

Substitusi...
x + 2y = 13
x + 2(-2/3) = 13
x - 4/3 = 13
x = 13 + 4/3
x = 43/3

————————————————
2)

3x + 5y = -7 —» 12x + 20y = -28
4x + 7y = -10 —» 12x + 21y = -30

Eliminasi...
12x + 21y = -30
12x + 20y = -28
————————— (-)
y = -2

Substitusi...
3x + 5y = -7
3x + 5(-2) = -7
3x - 10 = -7
3x = 3
x = 1

————————————————
3)

0,1x + 0,3y - 2,8 = 0
0,4x - 0,2y+ 1,2 = 0

Kalikan 10, menjadi...
x + 3y = 28 —» 4x + 12y = 112
4x - 2y = -12

Eliminasi...
4x + 12y = 112
4x - 2y = -12
———————— (-)
14y = 124
y = 124/14
y = 62/7

Substitusi...
x + 3y = 28
x + 3(62/7) = 28
x + 186/7 = 28
x = 28 - 186/7
x = 10/7

1)
x + 2y = 13
x - 4y = 17
------------------ -
6y = -4
y = -4/6
y = -2/3
x + 2y = 13
x + 2(-2/3) = 13
x - 4/3 = 13
x = 13 + 4/3
x = 39/3 + 4/3
x = 43/3

nilai x dan y adalah 43/3 dan -2/3

2)
3x + 5y = -7 (× 4)
4x + 7y = -10 (× 3)
12x + 20y = -28
12x + 21y = -30
------------------------ -
-y = 2
y = -2
3x + 5y = -7
3x + 5(-2) = -7
3x - 10 = -7
3x = -7 + 10
3x = 3
x = 3/3
x = 1

nilai x dan y adalah 1 dan -2

3)
0,1x + 0,3y - 2,8 = 0
0,4x - 0,2y + 1,2 = 0
0,1x + 0,3y = 2,8 (× 4)
0,4x - 0,2y = -1,2 (× 1)
0,4x + 1,2y = 11,2
0,4x - 0,2y = -1,2
-------------------------- -
1,4y = 12,4
y = 12,4/1,4
y = 8 12/14
y = 8 6/7

0,1x + 0,3y = 2,8
x/10 + 3/10(62/7) = 28/10
x/10 + 186/70 = 28/10
x/10 = 28/10 - 186/70
x/10 = 196/70 - 186/70
x/10 = 10/70
x = 10/70 × 10
x = 100/70
x = 1 30/70
x = 1 3/7

nilai x dan y adalah 1 3/7 dan 8 6/7