Question

solve ax + by = a+b/2 and 3x +5y= 4

Answer 1

$\textbf{Answer:}$

$ax + by = \frac{a + b}{2} \: ...(1) \\ \\ 3x + 5y = 4 \: ...(2) \\ \\ multiplying \: 1st \: equation \: by \: 5 \\ \\ 5ax + 5by = \frac{5(a + b)}{2} \: ...(3) \\ \\ multiply \: 2nd \: equation \: by \: b \\ \\ 3bx + 5by = 4b \: \: ....(4) \\ \\ subtracting \: (4) \: from(3) \: we \: get \\ \\ x(5a - 3b) = 5a + 5b - \frac{8b}{2} \\ \\ x(5a - 3b) = 5a + \frac{3b}{2} \\ \\ x = \frac{1}{2} \\ \\from \: 2nd \: equation \: we \: get \\ \\ 5y = 4 - 3x = 4 - \frac{3}{2} = \frac{5}{2} \\ \\ y = \frac{1}{2}$
$\textbf{Hope it helps you!}$