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

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

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x=3, y=2

x=2, y=3

x=1, y=2

x=4, y=1

answer is B.

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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.

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