Determine the point on the graph of the linear equation 2x+5y=19 whose ordinate is `1(1)/(2)` times its abscissa.

Explanation

Let x be the abscissa of the given line 2x+5y=19, then by given condition,
Ordinate `(y) = 1(1)/(2)xx` Abscissa
`implies " " y=(3)/(2)x`
On putting `y=(3)/(2)x` in given equation, we get
`2x+5((3)/(2))x=19`
`implies " " 4x+15x=19xx2`
`implies " " 4x+15x=38`
`implies " " 19x=38`
`implies " " x=(38)/(19)`
`therefore " " x=2`
On substituting the value of x in Eq. (i), we get
y=(3)/(2)xx2=3`
`implies " " y=3`
Hence, the required point is (2,3).