Question

If (a+b,a-b) is the solution of equation 3x + 2y = 20 and 4x-5y=42 , then the value of b is ?????????​

Answer 1

x = a+b

y = a- b

Put this value in eq 3x + 2y = 20 and 4x - 5y = 42

3x + 2y = 20

3(a+b) +2(a - b) = 20

3a +3b +2a - 2b = 20

5a + b = 20 ________________( 1 )

And

4x - 5y = 42

4(a+b) - 5(a-b) =42

4a + 4b - 5a +5b = 42

-a + 9b = 42

a = - 42 +9b

Put a = - 42 +9b in eq 1

5(- 42 +9b) +b = 20

-210 +45b + b = 20

46b = 20 +210

46b = 230

b = 230 /46

b = 5

.

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Answer 2

Answer: 5

Step-by-step explanation:

x = a+b

y = a- b

Put this value in eq 3x + 2y = 20 and 4x - 5y = 42

3x + 2y = 20

3(a+b) +2(a - b) = 20

3a +3b +2a - 2b = 20

5a + b = 20 ________________( 1 )

And

4x - 5y = 42

4(a+b) - 5(a-b) =42

4a + 4b - 5a +5b = 42

-a + 9b = 42

a = - 42 +9b

Put a = - 42 +9b in eq 1

5(- 42 +9b) +b = 20

-210 +45b + b = 20

46b = 20 +210

46b = 230

b = 230 /46

b = 5