Question

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

STEP 1 : Forming the two linear equations from the given data

Let the point $P(x,y)$ lies on the linear equation $2x+5y=19$

Linear equation is $2x+5y=19$ $...\left(1\right)$

We also know that ordinate of point $P\left(x,y\right)$ is $1\frac{1}{2}$ times its abscissa

$\Rightarrow y=1\frac{1}{2}x$

$\Rightarrow y=\frac{3}{2}x$ $...\left(2\right)$

STEP 2 : Solving the two equations

Substitute the value of $y=\frac{3}{2}x$ in equation $1$ we get,

$2x+5\times \frac{3}{2}x=19$

$2x+\frac{15}{2}x=19$

$\frac{4x+15x}{2}=19$

$19x=19\times 2=38$

$x=2$

Substituting $x=2$ in equation $2$ we get,

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

$y=3$

Therefore the coordinates of the point $P(x,y)$ is $(2,3)$.