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The solution of equations $3 x + 2 y = 10$ and $4 x - 2 y = 4$ is

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x = - 2

and

y = 2

x = 2

and

y = - 2

x = - 2

and

y = - 2

x = 2

and

y = 2

answer is D.

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Detailed Solution

3 x + 2 y = 10

and

4 x - 2 y = 4

Comparing with

a_{1} x + b_{1} y + c_{1} = 0

and

a_{2} x + b_{2} y + c_{2} = 0

, we get

a_{1} = 3,

b_{1} = 2

and

c_{1} = - 10

a_{2} = 4,

b_{2} = - 2

and

c_{2} = - 4

By cross-multiplication formula, we have

\frac{x}{b_{1} c_{2} - b_{2} c_{1}} = \frac{y}{c_{1} a_{2} - a_{1} c_{2}} = \frac{1}{b_{2} a_{1} - a_{2} b_{1}}

\frac{x}{(2) (- 4) - (- 2) (- 10)} = \frac{y}{(- 10) (4) - (3) (- 4)} = \frac{1}{(- 2) (3) - (4) (2)}

\frac{x}{- 8 - 20} = \frac{y}{- 40 + 12} = \frac{1}{- 6 - 8}

\frac{x}{- 28} = \frac{y}{- 28} = \frac{1}{- 14}

x = \frac{- 28}{- 14}

and

y = \frac{- 28}{- 14}

x = 2

and

y = 2

Therefore, 4 is the correct option.

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