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NCERT Exemplar Solutions Class 9 Mathematics Solutions for Linear Equations in Two Variables- Exercise 4.3 in Chapter 4 - Linear Equations in Two Variables

Question 2 Linear Equations in Two Variables- Exercise 4.3

Determine the point on the graph of the linear equation 2x + 5y = 19 whose ordinate is 1½ times its abscissa.

Answer:

From the question, we have,

2x + 5y = 19 …(i)

According to the question,

Ordinate is 1½ times its abscissa

⇒ y = 1½ x = (3/2) x

Substituting y = (3/2)x in eq. (i)

We get,

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

(19/2)x = 19

x = 2

Substituting x = 2 in eq. (i)

We get

2x + 5y = 19

2(2) + 5y = 19

y = (19 – 4)/5 = 3

Hence, we get x =2 and y = 3

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

Video transcript
"hello everyone i am sumanjali math tutor from leader learning welcome to question and answer session given question is determine the point on the graph of the linear equation 2x plus 5y equals to 19 whose ordinate is one whole 1 upon 2 times its abscissa okay so coming to the given question uh the given equation is 2x plus 5y equals to 19. this is the given equation given equation is 2x plus 5y equals to 19 and also there is one more point that is given in the problem whose ordinate is one one and a half times its abscissa okay so abscissa is nothing but x coordinate and ordinate is nothing but y coordinate okay so y value so given that so y value is one one and a half times its abscissa that is x value okay i am changing this uh this uh fraction uh this mixed refraction into improper fraction 2 1 0 2 plus 1 it is 3 upon 2 times x okay so now i am substituting substituting y is equals to 3 by 2 x x in equation in equation 2x plus 5y equals to 19 okay so this is 2x plus 5 into y value is 3 upon 2 x is equals to 19 okay so this is 2 x plus 5 3 0 15 upon 2 times x equals to 19 and if we take lcm so 2 2 4 x 4 x plus 15 x upon 2 equals to 19 okay so this is 19 x okay so this is 19 x 4 plus 15 it is 19 x upon 2 equals to 19 and 19 19 will be cancelled out okay so we can cancel 19 and 19 both are in the numerator that is y okay so therefore x value is is equals to 2 okay so now if we substitute if sub if we substitute substitute x is equals to 2 then so 2 into 2 plus 5 y equals to 19 so that 5 y equals to 19 minus 4 the value is 15 and y is equals to 15 by 5 the value is 3 okay so the given point determine the point the point on graph is point is equals to it is in the form of coordinate x comma y x value is 2 y value is 3 okay so that's all hope you understand if you have further questions reach us at comment section and subscribe to the channel leader learning for further queries thank you"
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