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Mathematics

Solve :

3x + 2y = 14

-x + 4y = 7

Linear Equations

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Answer

3x + 2y = 14 …………… (1)

-x + 4y = 7 …………… (2)

Multiply 1 in the first equation and 3 in the second equation, then add both equations.

(3x + 2y = 14) x 1

(-x + 4y = 7) x 3

3x+2y=143x+12y=2114y=14+2114y=35\begin{matrix} & 3x & + & 2y & = & 14 \ & -3x & + & 12y & = & 21 \ \hline & & & 14y & = & 14 + 21 \ \Rightarrow & & & 14y & = & 35 \end{matrix}

⇒ y = 3514\dfrac{35}{14}

⇒ y = 2.5

Substituting the value of y in equation (1), we get:

⇒ 3x + 2 ×\times 2.5 = 14

⇒ 3x + 5 = 14

⇒ 3x = 14 - 5

⇒ 3x = 9

⇒ x = 93\dfrac{9}{3}

⇒ x = 3

Hence, the value of x = 3 and y = 2.5.

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