Question

In the following, find the co-ordinates of the point whose abscissa is the solution of the first equation and ordinate is the solution of the second equation:
`(2"a")/(3) - 1 = "a"/(2); (15 - 4"b")/(7) = (2"b" - 1)/(3)`.

Answer 1

`(2"a")/(3) - 1 = "a"/(2); (15 - 4"b")/(7) = (2"b" - 1)/(3)`.
Now
`(2"a")/(3) - 1 = "a"/(2)`
`(2"a")/(3) - "a"/(2) = 1`
`(4"a" - 3"a")/(6) = 1`
`"a" = 6`
Again
`(15 - 4"b")/(7) = (2"b" - 1)/(3)`
45 - 12b = 14b - 7
45 + 7 = 14b + 12b
52 = 26b
2 = b
∴ The co-ordinates of the point (6, 2)