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Determine the point on the graph of the linear equation 2x + 5y = 19, whose ordinate is 1 1/2 times its abscissa

Solution:

Given, the equation is 2x + 5y = 19

The ordinate is 1 1/2 times its abscissa i.e.,x-coordinate

We have to determine the point.

Given, y = (3/2)x

On cross multiplication,

2y = 3x

x = (2/3)y

Put x = (2/3)y in the equation,

2(2/3)y + 5y = 19

(4/3)y + 5y = 19

(4y + 15y)/3 = 19

19y/3 = 19

y/3 = 1

y = 3

Put y = 3 in the equation,

2x + 5(3) = 19

2x + 15 = 19

2x = 19 - 15

2x = 4

x = 4/2

x = 2

Therefore, the point is (2, 3).

✦ Try This: Determine the point on the graph of the equation x + 3y = 9 whose x-coordinate is 7/2 times its ordinate.

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 4

NCERT Exemplar Class 9 Maths Exercise 4.3 Problem 2

Determine the point on the graph of the linear equation 2x + 5y = 19, whose ordinate is 1 1/2 times its abscissa

Summary:

In a two dimensional coordinate system (x, y), the x-coordinate is called abscissa and the y-coordinate is called the ordinate. The point on the graph of the equation 2x + 5y = 19 whose ordinate is 1 1/2 times its abscissa is (2, 3)

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