Question

If 2x +3y=7 & 3x +2y =3, then x+y=

0
1
2
3



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Answer 1

Given

• 2x + 3y = 7
• 3x + 2y = 3

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To Find

• x + y

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Solution

We need to first find the value of 'x' in 1st equation and use it in 2nd equation to obtain the value of 'y' and use it to find the constant value of 'x' in 1st equation.

$\implies 2x+3y = 7$

$\implies 2x = 7 - 3y$

$\implies x = \dfrac{7-3y}{2}$         (i)

$\implies 3(\dfrac{7-3y}{2} ) + 2y = 3$

$\implies \dfrac{21-9y}{2} + 2y = 3$

$\implies \dfrac{21-9y}{2} + \dfrac{2y\times 2}{1\times 2} = 3$

$\implies \dfrac{21-9y}{2} + \dfrac{4y}{2} = 3$

$\implies \dfrac{21-9y+4y}{2} = 3$

$\implies \dfrac{21-5y}{2} = 3$

$\implies 21-5y = 3\times 2$

$\implies 21-5y = 6$

$\implies -5y = 6 - 21$

$\implies -5y = -15$

$\implies 5y = 15$

$\implies y = \dfrac{15}{5}$

$\implies y = 3$       (ii)

Now let's substitute the value of 'y' in first equation.

$\implies 2x + 3(3) = 7$

$\implies 2x + 9 = 7$

$\implies 2x = 7-9$

$\implies 2x = -2$

$\implies x = \dfrac{-2}{2}$

$\implies x = -1$      (i)

∴ x = -1

∴ y = 3

Now, let's use the obtained values of 'x' and 'y' to find the final answer required.

⇒ x + y

⇒ -1 + 3

⇒ 2

∴ x + y = 2

∴ The answer is 2.

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Answer 2

Answer:

$\huge\bf\underline \red{\underline{Answer}}$

Given

2x + 3y = 7

3x + 2y = 3

________________________

To Find

x + y

________________________

Solution

We need to first find the value of 'x' in 1st equation and use it in 2nd equation to obtain the value of 'y' and use it to find the constant value of 'x' in 1st equation.

$\implies 2x+3y = 7$

$\implies 2x = 7 - 3y$

$\implies x = \dfrac{7-3y}{2}$         (i)

$\implies 3(\dfrac{7-3y}{2} ) + 2y = 3$

$\implies \dfrac{21-9y}{2} + 2y = 3$

$\implies \dfrac{21-9y}{2} + \dfrac{2y\times 2}{1\times 2} = 3$

$\implies \dfrac{21-9y}{2} + \dfrac{4y}{2} = 3$

$\implies \dfrac{21-9y+4y}{2} = 3$

$\implies \dfrac{21-5y}{2} = 3$

$\implies 21-5y = 3\times 2$

$\implies 21-5y = 6$

$\implies -5y = 6 - 21$

$\implies -5y = -15$

$\implies 5y = 15$

$\implies y = \dfrac{15}{5}$

$\implies y = 3$       (ii)

Now let's substitute the value of 'y' in first equation.

$\implies 2x + 3(3) = 7$

$\implies 2x + 9 = 7$

$\implies 2x = 7-9$

$\implies 2x = -2$

$\implies x = \dfrac{-2}{2}$

$\implies x = -1$      (i)

∴ x = -1

∴ y = 3

Now, let's use the obtained values of 'x' and 'y' to find the final answer required.

⇒ x + y

⇒ -1 + 3

⇒ 2

∴ x + y = 2

∴ The answer is 2.

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