Question

If 5x + 4y= 13 and 4x + 5y = 14, find the value of (x - y).​

Answer 1

x = 1

y = 2

x - y = -1

Explanation:

5x + 4y= 13, then 4y = 13 - 5x, then y = (13 - 5x)/4

4x + 5y = 14

substitute for y:

4x + 5(13 - 5x)/4 = 14

simplifying:

4x + (65 - 25x)/4 = 14

4x + 16.25 -6.25x = 14

-2.25x = -2.25

x = 1

y = (13 - 5)/4 = 2

Answer 2

x - y = - 1

Explanation:

Given the 2 equations

5x + 4y = 13 → (1)

4x + 5y = 14 → (2)

Subtract (2) from (1) term by term , that is

(5x - 4x) + (4y - 5y) = 13 - 14

x - y = - 1