Question

In the following, find the co-ordinates of the point whose abscissa is the solution of first equation and the ordinate is the solution of the second equation:

`(13 - 3x)/2 = (x + 3)/3` and `(13 - 14y)/7 = (6 - 3y)/4`

Answer 1

Given: `(13 - 3x)/2 = (x + 3)/3` and `(13 - 14y)/7 = (6 - 3y)/4`.

Step-wise calculation:

1. Solve for x:

3(13 – 3x) = 2(x + 3)   ...(Cross-multiply) 

39 – 9x = 2x + 6

39 – 6 = 2x + 9x

33 = 11x

x = 3

2. Solve for y:

4(13 – 4y) = 7(6 – 3y) (Cross-multiply)

52 – 16y = 42 – 21y

52 – 42 = –21y + 16y 

10 = –5y 

y = –2

The required point is (3, –2).