Question

Solve the equation :

x/3+5y=13;2x+y/2=19​

Answer 1

Step-by-step explanation:

$\frac{x}{3} + 5y = 13 \\ \frac{x + 15y}{3} = 13 \\ x + 15y = 39\: \: - - > (i) \\ 2x + \frac{y}{2} = 19 \\ \frac{4x + y}{2} = 19 \\ 4x + y = 38\: \: - - > (ii) \\ \\ multiply \: equation \: (i) \: by \: 4 \\ \\ 4x + 60y = 156\: \: - - > (iii) \\ eliminatimg \: equation \: (ii) \: in \: (iii) \\ \: \: \: \: \: \: \: \: \: \: \: 4x + 60y = 156 \\ \: \: \: \: 4x + y = 38 \\ - \: \: \: \: - \: \: \: \: \: \: \: - \\ - - - - - - - - - \\ 59y = 118 \\ y = 2 \\ \\ pu t\: the \: value \: of \: 'y'\: in \: equation \: (i) \\ x + 30 = 39 \\ x = 9$

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Answer 2

Answer:

$\frac{x}{3} + 5y = 13 \\ \frac{x + 15y}{3} = 13 \\ x + 15y = 13 \times 3 \\ x + 15y = 39 \\ \\ 2x + \frac{y}{2} = 19 \\ \frac{4x + y}{2} = 19 \\ 4x + y = 19 \times 2 \\ 4x + y = 38 \\ \\ x + 15y = 39 \\4x + y = 38 \\ \\ (x + 15y = 39) \times 4 \\ 4x + 60y = 156 \\ \\ 4x + 60y = 156 \\ 4x \: + \: \: y = \: \: \: 38 \\ ( - ) \: \: \: ( - ) \: \: \: ( - ) \\ - - - - - - - \\ 59y = 118 \\ y = \frac{118}{59} \\ \boxed{ \large y = \underline{ \underline{ \bf 2}}} \\ \\ 4x + y = 38 \\ 4x + 2 = 38 \\ 4x = 38 - 2 \\ 4x = 36 \\ x = \frac{36}{4} \\ \boxed{ \large x = \underline{ \underline{ \bf 9}}}$