Determine the point on the graph of the linear equation 2x+ 5y = 19
whose ordinate is 1 ½ times its abscissa.
Thinking Process
(i) Firstly, consider abscissa as x and ordinate as y and make a linear equation under the given condition.
(ii) Solving both linear equations to get the value of x and y.
(iii) Further, write the coordinates in a point form.
Let $x$ be the abscissa of the given line $2 x+5 y=19$, then by given condition,
Ordinate $(y)=1 \frac{1}{2} \times$ Abscissa
$\Rightarrow$ $y=\frac{3}{2} x$ $\ldots$ (i)
On putting $y=\frac{3}{2} x$ in given equation, we get
$2 x+5\left(\frac{3}{2}\right) x=19$
$\Rightarrow \quad 4 x+15 x=19 \times 2$
$\Rightarrow \quad 4 x+15 x=38$
$\Rightarrow \quad 19 x=38$
$\Rightarrow \quad x=\frac{38}{19}$
$\therefore \quad x=2$
On substituting the value of $x$ in Eq. (0), we get
$y=\frac{3}{2} \times 2=3$
$\Rightarrow \quad y=3$
Hence, the required point is $(2,3)$.