Question

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

• A. $(6,2)$
• B. $(7,4)$
• C. $(1,4)$
• D. $(2,3)$

Answer 1

The correct option is D $(2,3)$

As it is given that the ordinate is $1\frac{1}{2}$ times its abscissa

Then, we have $y=\frac{3}{2}x$ ..... $\left(i\right)$

Given : $2x+5y=19$

$\Rightarrow 2x+\frac{15}{2}x=19$ ...... From $\left(i\right)$

$\Rightarrow 19x=19\left(2\right)$

$\Rightarrow x=2$

From $\left(i\right)$, we get

$y=\frac{3}{2}\times 2=3$

$x=2,y=3$

Therefore, the required point is $(2,3)$.