Q179 / 270 · NDA 2013 (Phase 2) · Mathematics

If $8 x-9 y=20$ and $7 x-10 y=9$, then what is $2 x-y$ equal to?

  • Correct answer
    A
    10
  • B
    11
  • C
    12
  • D
    13

Solution

Substracting two given equations. $\begin{aligned} 8 x-9 y & =20 \\ 7 x-10 y & =9 \\ -\quad+\quad & - \\ \hline x+y & =11 \quad \text { or, } x=11-y \end{aligned}$ Plug in $x=11-y$ into $\begin{array}{r}8 x-9 y=20 \\ 8(11-y)-9 y=20 \\ 88-8 y-9 y=20\end{array}$ or, $17 y=68 \Rightarrow y=4$ and, $x=11-4=7$ $2 x-y=2(7)-4=10$

Hence, the correct answer is option: 'A'.

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