Which of the following is the solution for the given pair of linear equations?

$3 x 2 − 5 y 3 = − 2 and x 3 + y 2 = 136$

see full answer

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

x=3, y=2

x=2, y=3

x=1, y=2

x=4, y=1

answer is B.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Given equations are

3 x 2 − 5 y 3 = − 2 and x 3 + y 2 = 136

.
Let us find the value of y in terms of x for the equation

3 x 2 − 5 y 3 = − 2

3 x 2 − 5 y 3 = − 2 ⇒ − 5 y 3 = − 2 − 3 x 2 ⇒ − 5 y 3 = − 4 − 3 x 2 ⇒ y = − 35 − 4 − 3 x 2

Hence,

y = 12 + 9 x 10 .......... (1)

Obtaining the equation in a single variable for x by substituting value of y from eq (1) in

x 3 + y 2 = 136 ⇒ x 3 + 12 (12 + 9 x 10) = 136

We get,

x 3 + 1220 + 9 x 20 = 136

By solving, find the value of x.

x 3 + 1220 + 9 x 20 = 136 ⇒ x 3 + 9 x 20 = 136 − 35 ⇒ 20 x + 27 x 60 = 65 − 18 30 ⇒ 47 x 60 = 4730 ⇒ x 2 = 1

Thus, x = 2.
Now, let us find the value of y by substituting the value of x obtained into equation.

3 x 2 − 5 y 3 = − 2

3 x 2 − 5 y 3 = − 2 ⇒ 3 (2) 2 − 5 y 3 = − 2 ⇒ − 5 y 3 = − 2 − 3 ⇒ − 5 y 3 = − 5 ⇒ y 3 = 1

Thus, y=3.
By using the substitution method, the value of x=2 and the value of y=3.
Therefore, the correct option is 2.

Watch 3-min video & get full concept clarity