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:

3x – (1 – x) = 9 and `2y - 1 = 10 - (5y)/3`

Answer 1

Given: 3x – (1 – x) = 9 and `2y - 1 = 10 - (5y)/3`.

Step-wise calculation:

1. Solve for x:

3x – (1 – x) = 9 

⇒ 3x – 1 + x = 9

⇒ 4x – 1 = 9

⇒ 4x = 10

⇒ `x = 10/4` 

⇒ `x = 5/2` 

⇒ x = 2.5

2. Solve for y:

`2y - 1 = 10 - (5y)/3`

Multiply both sides by 3:

3(2y – 1) = 30 – 5y

⇒ 6y – 3 = 30 – 5y

⇒ 6y + 5y = 30 + 3

⇒ 11y = 33

⇒ `y = 33/11` 

⇒ y = 3

The coordinates of the point are `(5/2, 3)` i.e., (2.5, 3).