Question

find the value of x+y
Given 3x+y=7 and
2x+3y=8​

Answer 1

3x + y = 7 =≥ Equation 1

2x + 3y =≥ Equation 2

To find : x + y

EQUATION 1 :

3x + y = 7

By transposing (+3x) to the RHS (Right Hand Side)

y = 7 - 3x

EQUATION 2 :

Substituting the value of y as 7-3x

2x + 3y = 8

2x + 3(7-3x) = 8

2x + 21 - 9x = 8

adding the like terms,

21 - 7x = 8

Transposing (+21) to the RHS (Right Hand Side)

-7x = 8-21

-7x = (-13)

$x = \dfrac{ - 13}{ - 7}$

$x = \dfrac{13}{7}$

y = 7 - 3x

$y = 7 - 3( \dfrac{13}{7})$

$y = 7 - \dfrac{39}{7}$

$y = \dfrac{49 - 39}{7}$

$y = \dfrac{10}{7}$

VERIFICATION :

EQUATION 1 :

3x + y = 7

LHS :

3x + y

3x + y = 7

LHS :

$3( \dfrac{13}{7} ) + \dfrac{10}{7}$

$\dfrac{39}{7} + \dfrac{10}{7}$

$= \dfrac{39 + 10}{7}$

$= \dfrac{49}{7}$

By reducing to the lowest terms,

$= 7$

RHS :

= 7

Therefore LHS = RHS = 7

EQUATION 2 :

2x + 3y = 8

LHS :

2x + 3y

$2( \dfrac{13}{7}) + 3( \dfrac{10}{7})$

$= \dfrac{26}{7} + \dfrac{30}{7}$

$= \dfrac{26 + 30}{7}$

$= \dfrac{56}{7}$

By reducing to the lowest terms,

= 8

RHS :

= 8

LHS = RHS = 8

Hence verified

$x = \dfrac{13}{7}$

$y = \dfrac{10}{7}$

Answer 2

3x + y = 7

2x + 3y are the equations given.

To find : x + y

Let us look at each equation one by one.

EQUATION 1:

3x + y = 7

y = 7 - 3x

EQUATION 2:

Substituting the value of y as 7-3x

2x + 3y = 8

2x + 3(7-3x) = 8

2x + 21 - 9x = 8

21 - 7x = 8

-7x = 8-21

-7x =  (-13)

$x = \dfrac{ - 13}{ - 7}$

$x = \dfrac{13}{7}$

Therefore y :

y = 7 - 3x

$y = 7 - 3( \dfrac{13}{7})$

$y = 7 - \dfrac{39}{7}$

$y = \dfrac{49 - 39}{7}$

$y = \dfrac{10}{7}$

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VERIFICATION :

When we substitute the values of x and y respectively, the answer should be equal to the number in the Right side of the equation (also known as RHS)

3x + y = 7

3x + y = 7

$3( \dfrac{13}{7} ) + \dfrac{10}{7}$ = 7

$\dfrac{39}{7} + \dfrac{10}{7}$ = 7

$\dfrac{39 + 10}{7}$ = 7

$\dfrac{49}{7}$ = 7

Therefore LHS = RHS = 7

(NOTE :- If the answer matches after solving the first equation itself, we can conclude that x and y are found correctly, by for 100% verification, it is better to substitute in both the equations)

2x + 3y = 8

$2( \dfrac{13}{7}) + 3( \dfrac{10}{7})$ = 8

$\dfrac{26}{7} + \dfrac{30}{7}$ = 8

$\dfrac{26 + 30}{7}$ = 8

$\dfrac{56}{7}$ = 8

LHS = RHS = 8

Hence verified

$x = \dfrac{13}{7}$

$y = \dfrac{10}{7}$

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TO FIND : x + y

substituting the values,

$\dfrac{13}{7} + \dfrac{10}{7}$

$= \dfrac{13 + 10}{7}$

ANSWER =≥ $\dfrac{23}{7}$

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