Determine the point on the graph of the linear equation 2x + 5y = 19 w

1.	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.

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.