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Solve the pair of linear equations by cross-multiplication method

$2 x − 21 = 5 y, 3 + 4 y = − 3 x$

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x = 5 and y = − 1

x = 4 and y = − 4

x = 3 and y = − 3

x = 2 and y = − 1

answer is C.

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Detailed Solution

Given equations are

2 x − 5 y − 21 = 0 … (i) 3 x + 4 y + 3 = 0 … (i i)

In the cross multiplication method, for the system of equations.

a 1 x + b 1 y + c 1 = 0

and

a 2 x + b 2 y + c 2 = 0

the value variables are

x = b 1 c 2 − b 2 c 1 a 1 b 2 − a 2 b 1 and y = c 1 a 2 − c 2 a 1 a 1 b 2 − a 2 b 1

Determine the values of variables x and y.
On comparing the given equation with standard form, we get,

a 1 = 2, b 1 = − 5, c 1 = − 21 and a 2 = 3, b 2 = 4, c 2 = 3

Substituting the value of

a 1, b 1, c 1

and

a 2, b 2, c 2

, we get,

Therefore, the values of variables are

x = 3 and y = − 3

.
Hence, option (3) is correct.

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