Question

2x-3y=14 and 5x-2y=16.substituting​

Answer 1

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2x - 3y = 14 ....(i)

5x - 2y = 16 ....(ii)

From equation (i),

$\implies 2x - 3y = 14$

$\implies 2x = 3y + 14$

$\implies \bf x = \frac{3y + 14}{2}$ ....(a)

Now,

Substituting this value of x from (a) in equation (ii),

$\therefore \rm 5(\frac{3y + 14}{2}) - 2y = 16$

$\implies \rm \frac{15y + 70}{2} - 2y = 16$

$\implies \rm (\frac{15y + 70}{2}) - (\frac{2y}{1} \times \frac{2}{2}) = 16$

$\implies \rm \frac{15y + 70}{2} - \frac{4y}{2} = 16$

$\implies \rm \frac{15y + 70 - 4y}{2} = 16$

$\implies \rm \frac{11y + 70}{2} = 16$

$\implies \rm 11y + 70 = 16 \times 2$

$\implies \rm 11y + 70 = 32$

$\implies \rm 11y = 32 - 70$

$\implies \rm 11y = -38$

$\implies \rm \bf y = \frac{-38}{11}$

Substituting this value of y in equation,

$\therefore \rm x = \frac{3(\frac{-38}{11}) + 14}{2}$

$\implies \rm x = \frac{\frac{-114}{11} + 14}{2}$

$\implies \rm x = \frac{\frac{-114}{11} + \frac{14 \times 11}{11}}{2}$

$\implies \rm x = \frac{\frac{-114}{11} + \frac{154}{11}}{2}$

$\implies \rm x = \frac{\frac{40}{11}}{2}$

$\implies \rm x = \frac{40}{11} \times \frac{1}{2}$

$\implies \rm x = \frac{\cancel{40}}{11} \times \frac{1}{\cancel{2}}$

$\implies \rm \bf x = \frac{20}{11}$

Hence, the value of x = 20/11 and y = -38/11.