Question

Given that 3x+2y=5a+b and 4x-3y=a+7b, solve for y-x in terms of a and b.​

Answer 1

y - x = - 2 b

Explanation:

Given-

3 x + 2 y = 5 a + b...................(i)

4 x - 3 y = a + 7 b.....................(ii)

Multiply by 3 and 2 in equation (i) & (ii) respectively-

Add equation (iii) & (iv)-

9 x + 6 y = 15 a + 3 a...................(iii)

8 x - 6 y = 2 a + 14 b ...................(iv)

17 x = 17 a + 17 b

x = a + b

Put x = a + b in equation (i)-

2 y = 5 a + b - 3 a - 3 b

2 y = 2 a - 2 b

y = a - b

∴ y - x = a - b - ( a + b )

y - x = a - b - a - b

y - x = - 2 b