Determine the point on the graph of the linear equation 2x + 5y = 19 whose ordinate is times its abscissa.

Given: 2x + 5y = 19…………(i)

ordinate is times its abscissa

⇒ y = x = x

Putting y = x in eq. (i)

We have

2x + 5 x = 19
.

Putting x = 2 in eq. (i)

We have

2x2 + 5y = 19

y = = 3.

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