Question

In each of the following, find the coordinates of the point whose abscissa is the solution of the first equation and ordinate is the solution of the second equation.

(7 - x) + 7x = `(x + 5); (2 + 3y)/(2)` = 2y - 6

Answer 1

For abscissa,
(7 - x) + 7x = (x + 5) ....(given)
7 - x + 7x = x + 5
6x - x = 5 - 7
5x = -2

∴ x = `-(2)/(5)`
For ordinate,

`(2 + 3y)/(2)` = 2y - 6 ....(given)

2 + 3y = 2(2y - 6)
2 + 3y = 4y - 12
3y - 4y = -12 - 2
-y = -14
∴ y = 14
∴ The coordinates of the point are `(-2/5, 14)`.