Question

15x+17y=183 25+13y=213​

Answer 1

Required solution: x = $\dfrac{27}{5}$ and y = 6.

Step-by-step explanation:

We will solve the equations by Substitution Method.

The given equations are

15x + 17y = 183 ... ... (1)

25x + 13y = 213 ... ... (2)

From (1), we get

15x = 183 - 17y

⇒ x = $\dfrac{183-17y}{15}$ ... ... (3)

Substituting x = $\dfrac{183-17y}{15}$ in (2), we get

$25\times\dfrac{183-17y}{15}$ + 13y = 213

⇒ $\dfrac{5}{3}$ (183 - 17y) + 13y = 213

⇒ $\dfrac{915-85y+39y}{3}$ = 213

⇒ 915 - 46y = 639

⇒ 46y = 276

⇒ y = 6

Putting y = 6 in (3), we get

x = $\dfrac{183-17(6)}{15}$

= $\dfrac{183-102}{15}$

= $\dfrac{81}{15}$

= $\dfrac{27}{5}$

∴ the required solution is x = $\dfrac{27}{5}$ and y = 6.

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