Question : If $6x–5y=13,7x+2y=23$, then $11x+18y=?$
Option 1: –15
Option 2: 51
Option 3: 33
Option 4: 15
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Correct Answer: 51
Solution :
⇒Given: $6x–5y=13$
⇒ $2×(6x–5y)=13×2$
⇒ $(12x–10y)=26$ ---------------------------------(1)
$7x+2y=23$
⇒ $5×(7x+2y)=23×5$
⇒ $(35x+10y)=115$ ------------------------------(2)
Adding equations (1) and (2), we have,
$(12x–10y+35x+10y)=26+115$
⇒ $47x=141$
$\therefore x=\frac{141}{47}=3$
Putting the value of $x$ in $7x+2y=23$, we have,
$7×3+2y=23$
⇒ $2y=23–21$
$\therefore y=1$
So, $11x+18y=11×3+18×1=33+18=51$
Hence, the correct answer is 51.
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