simultaneous equations help?

15 (20a + 3b = 48)
20 (15a + 7b = 55)
------------------

300a + 45b = 720

300a + 140b = 1100
-----------------------
MINUS

-95b = -380

b = 4 <<<<<<<<<< And now put this in either one of your equation:

20a + 3(4) = 48

20a + 12 = 48

20a = 36

a = 9/5

Solution a = 9/5 and b = 4

1st & 2nd equations simplified in terms of b:
20a + 3b = 48
3b = 48 - 20a
b = (48 - 20a)/3

15a + 7b = 55
7b = 55 - 15a
b = (55 - 15a)/7

1st & 2nd equations to find a:
7(48 - 20a) = 3(55 - 15a)
336 - 140a = 165 - 45a
95a = 171
a = 171/95 or 9/5

1st equation to find b:
= (48 - 20[9/5])/3
= (48 - 36)/3
= 12/3 or 4

Answer: a = 9/5, b = 4

Proof (2nd equation):
15(9/5) + 7(4) = 55
27 + 28 = 55
55 = 55

- 60a - 9b = - 144
60a + 28b = 220----ADD

19 b = 76
b = 4

20a + 12 = 48
20a = 36
a = 9 / 5

a = 9 / 5 , b = 4

4

9/5


plez answer mine:

http://answers.yahoo.com/question/index;_ylt=Ak49owujxuvAoB9Nqr82cWnsy6IX;_ylv=3?qid=20081130054606AAHVPs0

20a + 3b = 48 (solve by using substitution)
15a + 7b = 55

15a + 7b = 55
15a = 55 - 7b
a = (55 - 7b)/15

20a + 3b = 48
20[(55 - 7b)/15] + 3b = 48
4(55 - 7b)/3 + 3b = 48
3[(220 - 28b)/3 + 3b] = 3[48]
220 - 28b + 9b = 144
-28b + 9b = 144 - 220
-19b = -76
b = -76/-19
b = 4

20a + 3b = 48
20a + 3(4) = 48
20a + 12 = 48
20a = 48 - 12
20a = 36
a = 36/20
a = 9/5 (1.8)

∴ a = 9/5 (1.8) , 4

b=4

3 x 20a + 3b = 48 => 60a + 9b = 144 ----- (1)
4 x 15a + 7b = 55 => 60a + 28b = 220 ---- (2)

(2) - (3) => 0b + 19b = 76

=> b = 76/19

=> b = 4

20a + 3b = 48 Eq. (1)
15a + 7b = 55 Eq. (2)

140a + 21b = 336 Eq. (1) x 7
45a + 21b = 165 Eq. (2) x 3
-----subtract-------------------------
95a = 171
a = 171/95 = 9/5

60a + 28b =220 Eq. (2) x 4
60a + 9b = 144 Eq. (1) x 3
-----subtract------------------------
19b = 76
b = 76/19
b = 4

(a, b) = (9/5, 4)

its a little messy

20a + 3b = 48
20a = 48 - 3b
a = (48 - 3b)/20

15a + 7b = 55
15((48-3b)/20) + 7b = 55
0.75(48-3b) + 7b = 55
36 - 2.25b + 7b = 55
4.75b = 55 - 36 = 19
b = 19/4.75 = 4

20a + 3b = 48
20a + 3*4 = 48
20a = 48 - 12
20a = 36
a = 1.8