Practicing Success
Linear equations $3x+5y=19$ and $10x-3y=24$ have solution $x =\frac{α}{3}$ and $y =\frac{β}{2}$, then the value of $α+β$ is: |
5 13 10 7 |
13 |
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 ------------------------ 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 |