Q. 383.7( 7 Votes )

# Solve for x and y:

Answer :

We have

and

Lets simplify these equations. Assuming p = 1/(3x + 2y) and q = 1/(3x – 2y),

2p + 3q = 17/5

⇒ 10p + 15q = 17 …(i)

Also,

⇒ 5p + q = 2 …(ii)

To solve these equations, we need to make one of the variables (in both the equations) have same coefficient.

Multiply equation (ii) by 2, so that the variable p in both the equations have same coefficient.

Recalling equations (i) and (ii),

10p + 15q = 17

5p + q = 2 [×2

⇒ 13q = 13

⇒ q = 1

Substitute q = 1 in eq.(i)/eq.(ii), as per convenience of solving.

Thus, substituting in eq.(ii), we get

5p + 1 = 2

⇒ 5p = 1

⇒ p = 1/5

Thus, p = 1/5 and q = 1

As p = 1/(3x + 2y),

⇒

⇒ 3x + 2y = 5 …(iii)

And q = 1/(3x – 2y)

⇒

⇒ 3x – 2y = 1 …(iv)

Adding equations (iii) and (iv) to obtain x and y,

(3x + 2y) + (3x – 2y) = 5 + 1

⇒ 6x = 6

⇒ x = 1

Putting the value of x in equation (iv), we get

3(1) – 2y = 1

⇒ 3 – 2y = 1

⇒ 2y = 2

⇒ y = 1

Hence, we have x = 1 and y = 1

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Solve the following pair of linear equation by cross - multiplication method:

x + 4y + 9 = 0

5x – 1 = 3y

KC Sinha - Mathematics