Question

(ii) 3x+4y= 10 and 2 x – 2y=2
(IV) x\2+y\3=-1 and x-y\3=3​

Answer 1

$\color{red}{\large\underline{\underline\mathtt{Question:}}}$

• $\mathtt{3x + 4y = 10 [Equation..1]}$

$\mathtt{2x - 2y = 2 [Equation..2]}$

• $\mathtt{\dfrac{x}{2} + \dfrac{y}{3} = (-1) [Equation..1]}$

$\mathtt{\dfrac{x - y}{3} = 3 [Equation..2]}$

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$\color{purple}{\large\underline{\underline\mathtt{To\:Find:}}}$

→ $\textit{The value of x and y}$

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$\color{blue}{\large\underline{\underline\mathtt{Concept:}}}$

• $\textit{In equation 1 , the equation can be solved}$ $\textit{by using elimination method}$
• $\textit{In equation 2 , the equation can be solved}$ $\textit{by solving the equation first}$$\textit{and then using the elimination method}$

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$\color{magenta}{\large\underline{\underline\mathtt{Solution:}}}$

• $\mathtt{3x + 4y = 10}$
• $\mathtt{2x - 2y = 2}$

$\textit{By using elimination method ,we get}$

☞$3x + 4y = 10 \times (2)$

$2x - 2y = 2 \times (3)$

☞$6x + 8y = 20$

$6x - 6y = 6$

$By\:subtracting$

☞$\cancel{+ 6x} + 8y = 20$

$\cancel{- 6x} - 6y = 6$

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$14y = 14$

$\therefore y = 1$

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$\textsf{Putting the value in the equation 1, we get}$

$6x + 8y = 20$

$\Rightarrow 6x + 8 \times (1) = 20$

$\Rightarrow 6x + 8 = 20$

$\Rightarrow 6x = 20 - 8$

$\Rightarrow 6x = 12$

$\Rightarrow x = \dfrac{12}{6}$

$\Rightarrow x = \dfrac{\cancel{12}}{\cancel{6}}$

$\Rightarrow x = 2$

$\therefore x = 2$

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• $\mathtt{\dfrac{x}{2} + \dfrac{y}{3} = (-1)}$

$\mathtt{\dfrac{x - y}{3} = 3 }$

$\textit{By solving the equation ,we get}$

$Equation..1$

$\Rightarrow \dfrac{3x + 2y}{6} = (-1)$

$\Rightarrow 3x + 2y = (-1) \times 6$

$\Rightarrow 3x + 2y = (-6) [Equation...(i)]$

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$Equation..2$

$\Rightarrow \dfrac{x - y}{3} = 3$

$\Rightarrow x - y = 3 \times 3$

$\Rightarrow x - y = 9 [Equation..(ii)$

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$\textsf{By putting the two equations together , we get}$

☞$3x + 2y = (-6)$

$x - y = 9$

$\textit{By using elimination method ,we get}$

☞$3x + 2y = (-6) \times 1$

$x - y = 9 \times 2$

☞$3x + 2y = (-6)$

$2x - 2y = 18$

$By\:Adding$

☞$3x \cancel{+ 2y} = (-6)$

$2x \cancel{- 2y} = 18$

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$5x = 12$

$x = \dfrac{12}{5}$

$\therefore x = \dfrac{12}{5}$

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$\textsf{Putting the value in the equation (i) , we get}$

$\Rightarrow 3 \times \dfrac{12}{5} + 2y = (-6)$

$\Rightarrow \dfrac{12}{5} + 2y = \dfrac{(-6)}{3}$

$\Rightarrow 2y = \dfrac{(-6)}{3} - \dfrac{12}{5}$

$\Rightarrow 2y = \dfrac{(-30) - 36}{15}$

$\Rightarrow 2y = \dfrac{(-66)}{15}$

$\Rightarrow 2y \times 15 = (-66)$

$\Rightarrow 30y = (-66)$

$\Rightarrow y = \dfrac{(-66)}{30}$

$\Rightarrow y = \dfrac{\cancel{(-66)}}{\cancel{30}}$

$\Rightarrow y = \dfrac{(-33)}{15}$

$\Rightarrow y = \dfrac{\cancel{(-33)}}{\cancel{15}}$

$\Rightarrow y = \dfrac{(-11)}{5}$

$\therefore y = \dfrac{(- 11)}{5}$

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Answer 2

Answer:

1) answer :

3x+4y=10

2x-2y=2 multiply 2 in the equation 2

4x-4y=8

solve this equation

7x=18

x=18/7

put the value in eqn 1 u get y OK friend