Math, asked by khiradeprashik67, 6 months ago

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

Answers

Answered by AstroPaleontologist
0

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}

Answered by Dinosaurs1842
3

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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