Solve for x and y
x/2 - y/9 =6
x/7 + y/3=5
Answers
x/7+y/3=5 equation (1)
x/2-y/9=6 equation (2)
x/7+y/3 =5 add
3x+7y=105 equation( 1)
x/2-y/9=6 add
9x-2y=108 equation (2)
3x+7y=105 multiply by 2
9x-2y=108multiply by 7
6x+14y=210
63x-14y=756
69x=966
x=14
6×14+14y=210
84+14y=210
14y=210-84
14y=126
y=9
so x=14
y=9
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1) x/7 + y/3 = 5 x/2 - y/9 = 6
On taking LCM of denominators and simplifying, we get the linear equations as
3x + 7y = 105 → (1)
9x − 2y = 108 → (2)
Multiply equation(1) with 3 , we get
9x + 21y = 315 → (3)
Now subtract (2) from (3)
9x + 21y = 315
9x − 2y = 108
----------------------
23y = 207
∴ y = (207/23) = 9
Put y = 9 in 3x + 7y = 105
3x + 7(9) = 105
⇒ 3x = 105 − 63 = 42
∴ x = (42/3) = 14
2) 4x + 6/y = 15
3x - 4/y = 7
put (1/y) = p
Hence the above equations become,
4x + 6p =15 → (1)
3x − 4p = 7 → (2)
Multiply equation (1) with 4 and equation (2) with 6 and add as shown
16x + 24p = 60
18x − 24p = 42
----------------------
34x = 102
∴ x = (102/34) = 3
Put x = 3 in 4x + 6p =15
4(3) + 6p = 15
12 + 6p = 15
6p = 3
∴ p = (3/6) = (1/2)
⇒ (1/y) = (1/2)
∴ y = 2