Question

11 x + 13 y = 74 and 13 x + 11 y = 70 then 10( x+ y) is ---

Answer 1

Answer

To find the answer of this question, first we should find the values of x and y. To find the values of those variables x and y, we use the substitution method.

$\sf \dashrightarrow 11x + 13y = 74 \: \: --- (i)$

$\sf \dashrightarrow 13x + 11y = 70 \: \: --- (ii)$

By taking first equation,

$\sf \dashrightarrow 11x + 13y = 74$

$\sf \dashrightarrow 11x = 74 - 13y$

$\sf \dashrightarrow x = \dfrac{74 - 13y}{11}$

Now, we can find the value of y by second equation.

$\sf \dashrightarrow 13x + 11y = 70$

$\sf \dashrightarrow 13 \bigg( \dfrac{74 - 13y}{11} \bigg) + 11y = 70$

$\sf \dashrightarrow \dfrac{962 - 169y}{11} + 11y = 70$

$\sf \dashrightarrow \dfrac{962 - 169y + 121y}{11} = 70$

$\sf \dashrightarrow \dfrac{962 - 48y}{11} = 70$

$\sf \dashrightarrow 962 - 48y = 70 \times 11$

$\sf \dashrightarrow 962 - 48y = 770$

$\sf \dashrightarrow -48y = 770 - 962$

$\sf \dashrightarrow -48y = -192$

$\sf \dashrightarrow y = \dfrac{-192}{-48}$

$\sf \dashrightarrow y = 4$

Now, let's find the value of x by first equation.

$\sf \dashrightarrow 11x + 13y = 74$

$\sf \dashrightarrow 11x + 13(4) = 74$

$\sf \dashrightarrow 11x + 52 = 74$

$\sf \dashrightarrow 11x = 74 - 52$

$\sf \dashrightarrow 11x = 22$

$\sf \dashrightarrow x = \dfrac{22}{11}$

$\sf \dashrightarrow x = 2$

Now, let's find the answer of this question.

$\sf \dashrightarrow 10 (x + y)$

$\sf \dashrightarrow 10 (2 + 4)$

$\sf \dashrightarrow 10 (6)$

$\sf \dashrightarrow 60$

Hence, the answer is 60.