Q. 4 C5.0( 4 Votes )

# Let us solve the following simultaneous equations in two variables by the method of substitution and check whether the solutions satisfy the equations.

Answer :

Given … (1)

And … (2)

Expressing x of equation (1) in terms of y,

⇒ x + y = 3xy

∴ x = 3xy – y … (3)

Substituting (3) in (2),

⇒ 3xy – 2y = xy

⇒ 3xy – xy = 2y

⇒ 2xy = 2y

∴ x = 1

Substituting x value in (3),

⇒ x = 3xy – y

⇒ 1 = 3(1) y – y

⇒ 1 = 3y – y

⇒ 1 = 2y

∴ y = 1/2

∴ By solving, x = 1 and y = 1/2.

__Justification:__

(1) -

⇒ 3 = 3

And (2) -

⇒ 1 = 1

∴ We can see that x = 1 and y = 1/2 satisfy equations (1) and (2).

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