Determine the point on the graph of the linear equation 2x + 5y =… - Vidyadip

Question

Determine the point on the graph of the linear equation 2x + 5y = 19 whose ordinate is $1\frac{1}{2}$ times its abscissa.

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Answer

Let x be the abscissa of the given line 2x + 5y = 19, then by given condition, Ordinate $\text{(y)}=1\frac{1}{2}\times\text{Abscissa}$
$\Rightarrow\text{y}=\frac{3}{2}\text{x}\ ....(\text{i})$
On putting $\text{y}=\frac{3}{2}\text{x}$ in given equation, we get
$2\text{x}+5\Big(\frac{3}{2}\Big)\text{x}=19$
$\Rightarrow4\text{x}+15\text{x}=19\times2$
$\Rightarrow4\text{x}+15\text{x}=38$
$\Rightarrow 19\text{x}=38$
$\Rightarrow\text{x}=\frac{38}{19}$
$\therefore\text{x}=2$
On substituting the value of x in Eq. (i) we get
$\text{y}=\frac{3}{2}\times2=3$
$\Rightarrow\text{y}=3$
Heanse, the required point is (2, 3).

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