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Solve the following pair of simultaneous equations: $\frac{x}{3} = \frac{y}{2}; \frac{2 x}{3} - \frac{y}{2} = 2$ .

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An Intiative by Sri Chaitanya

(- 3, 4)

(1, 9)

(6, 4)

(3, 8)

answer is C.

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Detailed Solution

Given that,

\frac{x}{3} = \frac{y}{2}; \frac{2 x}{3} - \frac{y}{2} = 2

.
The equation

\frac{x}{3} = \frac{y}{2}

can be rewritten as:

\frac{x}{3} = \frac{y}{2}

\Rightarrow 2 x = 3 y

\Rightarrow 2 x - 3 y = 0 . . . . . . . . . (1)

The equation

\frac{2 x}{3} - \frac{y}{2} = 2

can be written as:

\frac{2 x}{3} - \frac{y}{2} = 2

\Rightarrow \frac{4 x - 3 y}{6} = 2

\Rightarrow 4 x - 3 y = 12 . . . . . . . . . (2)

Subtracting equation (2) from equation (1) to eliminate

y

, because the coefficients of

y

are the same. So, we get,

(4 x - 2 x) + (- 3 y + 3 y) = 12 - 0

2 x = 12

x = 6

Substituting

x = 6

in the equation 1, we get,

12 - 3 y = 0

3 y = 12

y = 4

Therefore, option (3) is correct.

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