Question

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

Answer 1

Let x be the abscissa of the required point on the line 2x + 5y = 19.
then by given condition,
Ordinate, $y=1\frac{1}{2}\times x$
$\Rightarrow y=\frac{3}{2}x$
On putting $y=\frac{3}{2}x$ in given equation, we get,
$2x+5\left(\frac{3}{2}\right)x=19\Rightarrow 4x+15x=19\times 2\Rightarrow 4x+15x=38\Rightarrow 19x=38\Rightarrow x=\frac{38}{19}\therefore x=2$
On Substituting the value of x,
$y=\frac{3}{2}\times 2=3$
$\Rightarrow y=3$
Hence, the required point is (2, 3).