Question

Solve simultaneously the folowing system of linear equations

$2x+y=6$, $7x+2y=27$

• A. $(-5,4)$
• B. $(4,-2)$
• C. $(5,4)$
• D. $(5,-4)$

Answer 1

The correct option is D $(5,-4)$

Let $2x+y=6$........(1)

and $7x+2y=27$.......(2)

Multiply the (1) by $2$

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

Subtract the (3) from (2), we get

$\Rightarrow 4x+2y=12$

$\Rightarrow 7x+2y=27$

- - -

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$-3x=-15$

$\Rightarrow x=\frac{-15}{-3}=5$

Substitute the value of $x=5$ in (1)

$\Rightarrow 2\times 5+y=6$

$\Rightarrow 10+y=6$

$\Rightarrow y=6-10=-4$

So, $x=5$ and $y=-4$