Linear equations 3x+5y=19 and 10x-3y=24 have solution x =(α)/3 and y…

3x + 5y = 19    ----(1)

10x - 3y = 24   ----(2)

Multiply equation 1 by 3 and equation 2 by 5 , and then add them

( 3x + 5y = 19 ) × 3

( 10x - 3y = 24 ) × 5

9x + 15y = 57

50x - 15y = 120

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59x = 177

x = 3

Now, Put value of x into equation 1

3 × 3 + 5y = 19

5y = 10

y = 2

Now,  x = \(\frac{α}{3}\) , y = \(\frac{β}{2}\)

3 = \(\frac{α}{3}\) , 2 = \(\frac{β}{2}\)

So, α = 9 , β= 4

Now, α + β = 9 + 4 = 13