Question

1.x/4 + y/3 = 5/12

x/2 + y = 1
nilai x + y

2. 8/x + 3/y = 3
4/x + 9/y = 4

x ? y ?

3. 3x+y+z=7
2x+y-z=3
x+y+z=3
nilai x,y,z ?

4. 3x+2y+z=12
4x +3y+2z=17
x+y+3z= 5
x+y+z ?

5. x + y = 7
y - z = 9
y + z = 11
x^2?

Answer 1

1) x/4 + y/3 = 5/12
____________ ×12
=> 3x + 4y = 5
x/2 + y/1 = 1
_________ ×2
=> x + 2y = 2

3x + 4y = 5 |×1|
x + 2y = 2 |×2|
=> 3x + 4y = 5
2x + 4y = 4 -
________
x = 1

x + 2y = 2
1 + 2y = 2
2y = 1
y = ½

x + y
=> 1 + ½
=> 1½

2) 8/x + 3/y = 3
4/x + 9/y = 4
Misal :
a = 1/x
b = 1/y
=> 8a + 3b = 3 |×3|
4a + 9b = 4 |×1|
=> 24a + 9b = 9
4a + 9b = 4 -
__________
20a = 5
a = ¼
8a + 3b = 3
8(¼) + 3b = 3
3b = 3 - 2
b = ⅓

a = 1/x
¼ = 1/x
x = 4
b = 1/y
⅓ = 1/y
y = 3
=> x = 4
y = 3

3) 3x+y+z=7
2x+y-z=3
x+y+z=3
=>
1) 3x + y + z = 7
2x + y - z = 3 +
__________
5x + 2y = 10
2) 3x + y + z = 7
x + y + z = 3 -
__________
2x = 4
x = 2
3) 5x + 2y = 10
5(2) + 2y = 10
10 + 2y = 10
2y = 0
y = 0
4) 3x + y + z = 7
3(2) + 0 + z = 7
6 + 0 + z = 7
z = 7 - 6
z = 1
=> x = 2
y = 0
z = 1

4) 3x+2y+ z=12
4x +3y+2z=17
x+ y+3z= 5
=>
1) 3x + 2y + z = 12 |×2|
4x + 3y + 2z = 17 |×1|
=> 6x + 4x + 2z = 24
4x + 3y + 2z = 17 -
_____________
2x + y = 7
2) 3x + 2y + z = 12 |×3|
x + y + 3z = 5 |×1|
=> 9x + 6y + 3z = 36
x + y + 3z = 5 -
_____________
8x + 5y = 31
3) 2x + y = 7 |×4|
8x + 5y = 31 |×1|
=> 8x + 4y = 28
8x + 5y = 31 -
_________
-y = -3
y = 3
4) 8x + 5y = 31
8x + 5(3) = 31
8x = 31 - 15
8x = 16
x = 2
5) 3x + 2y + z = 12
3(2) + 2(3) + z = 12
6 + 6 + z = 12
z = 12 - 12
z = 0
=> x+y+z
=> 2 + 3 + 0
=> 5

5) x + y = 7
y - z = 9
y + z = 11
=> 1) y - z = 9
y + z = 11 +
_______
2y = 20
y = 10
2) y - z = 9
10 - z = 9
z = 1
3) x + y = 7
x + 10 = 7
x = -3
=> x²
=> (-3)²
=> 9