Question

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Solve the following pair of linear equations by the substitution method :-
$\frac{3x}{2} - \frac{5y}{3} = - 2 \\ \frac{x}{3} + \frac{y}{2} = \frac{13}{6}$

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Answer 1

EXPLANATION.

Pair of linear equations.

⇒ 3x/2 - 5y/3 = - 2. - - - - - (1).

⇒ x/3 + y/2 = 13/6. - - - - - (2).

As we know that,

From equation (1) & (2), we get.

⇒ 9x - 10y = - 12. - - - - - (1).

⇒ 2x + 3y = 13. - - - - - (2).

Multiply equation (1) by 3, we get.

Multiply equation (2) by 10, we get.

⇒ 9x - 10y = - 12. - - - - - (1). x 3.

⇒ 2x + 3y = 13. - - - - - (2). x 10.

We get,

⇒ 27x - 30y = - 36. - - - - - (3).

⇒ 20x + 30y = 130. - - - - - (4).

Adding equation (3) & (4), we get.

⇒ 47x = 94.

⇒ x = 2.

Put the value of x = 2 in equation (1), we get.

⇒ 9x - 10y = - 12. - - - - - (1).

⇒ 9(2) - 10y = - 12.

⇒ 18 - 10y = - 12.

⇒ - 10y = - 12 - 18.

⇒ - 10y = - 30.

⇒ 10y = 30.

⇒ y = 3.

Values of x = 2 & y = 3.

Answer 2

Given :-

3x/2 - 5y/3 = -2

9x - 10y/6 = -2

9x - 10y = -2 × 6

9x - 10y = -12 (1)

x/3 + y/2 = 13/6

2x + 3y/6 = 13/6

2x + 3y = 13 (2)

Multiply the equation 1 by 3

3(9x - 10y) = 3(-12)

27x - 30y = -36

Multiply the equation 2 by 10

10(2x + 3y) = 10(13)

20x + 30y = 130

Add both

27x - 30y + 20x + 30y = -36 + 130

27x + 20x = -94

47x = -94

x = -94/47

x = -2

Using 2

2x + 3y = 13

2(-2) + 3y = 13

-4 + 3y = 13

3y = 13 - 4

3y = 9

y = 9/3

y = 3

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