The solution of 30x+34y=42 and 34x+30y=22 is ________
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Step-by-step explanation:
30x+34y=42
Dividing the equation by 2, we get
15x + 17y = 21 (1)
34x+30y=22
Dividing the equation by 2, we get
17x + 15y = 22 (2)
Multiplying (1) by 17 and (2) by 15
17(15x + 17y) = 17(21)
255x + 289y = 357 (3)
15(17x + 15y) = 15(22)
255x + 225y = 330 (4)
Subtracting (4) from (3), we get
255x + 289y = 357
+255x + 225y = 330
- - -
64y = 27
y = 27/64
Substituting y = 27/64 in (1), we get
15x + 17(27/64) = 21
15x + 459/64 = 21
(960x + 459)/64 = 21
960x + 459 = 1344
960x = 885
x = 885/960
x = 177/192
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