15/a+2/b = 17 , 1/a+1/b=36/5 find a+b
Answers
Step-by-step explanation:
Substituition method solve
15/x + 2/y = 17 , 1/x + 1/y = 36/5
lets take a and b = x and y
15/ x + 2/y = 17 , 1/x + 1/y = 36/5
Solution:
15/ x + 2/y = 17
1/x + 1/y = 36/5
Let 1/x = a and 1/y = b
15 a + 2 b = 17 -------- (1)
a+b = 36/5
5(a+b)=36
5 a + 5 b = 36 -------- (2)
There are two unknowns in the given equations. By solving these equations we have to find the values of a and b.
For that let us consider the coefficients of x and y in both equation.
In the first equation we have + 15a and in the second equation also we have + 5a and the symbols are same so we have to subtract them for eliminating the variable a.
15 a + 2 b = 17
(2) x 3 => 15 a + 15 b = 108
(-) (-) (-)
----------------
-13 b = -91
b = 91/13
b = 7
now we have to apply the value of b in either given equations to get the value of another variable x
Substitute b = 7 in the first equation
15 a + 2(7) = 17
15 a + 14 = 17
15 a = 17 – 14
15a = 3
a = 3/15
a = 1/5
Solution
x = 5
y = 1/7
verification:
15/ x + 2/y = 17
15/5 + 2/7 = 17
3 + [2/(1/7)] = 17
3 + 14 = 17
17 = 17
Step-by-step explanation:
15/ x + 2/y = 17
1/x + 1/y = 36/5
Let 1/x = a and 1/y = b
15 a + 2 b = 17 -------- (1)
a+b = 36/5
5(a+b)=36
5 a + 5 b = 36 -------- (2)
There are two unknowns in the given equations. By solving these equations we have to find the values of a and b. For that let us consider the coefficients of x and y in both equation. In the first equation we have + 15a and in the second equation also we have + 5a and the symbols are same so we have to subtract them for eliminating the variable a.
15 a + 2 b = 17
(2) x 3 => 15 a + 15 b = 108
(-) (-) (-)
----------------
-13 b = -91
b = 91/13
b = 7
now we have to apply the value of b in either given equations to get the value of another variable x
Substitute b = 7 in the first equation
15 a + 2(7) = 17
15 a + 14 = 17
15 a = 17 – 14
15a = 3
a = 3/15
a = 1/5
Solution
x = 5
y = 1/7
verification:
15/ x + 2/y = 17
15/5 + 2/7 = 17
3 + [2/(1/7)] = 17
3 + 14 = 17
17 = 17