find the value of x+y
Given 3x+y=7 and
2x+3y=8
Answers
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)
y = 7 - 3x
VERIFICATION :
EQUATION 1 :
3x + y = 7
LHS :
3x + y
3x + y = 7
LHS :
By reducing to the lowest terms,
RHS :
= 7
Therefore LHS = RHS = 7
EQUATION 2 :
2x + 3y = 8
LHS :
2x + 3y
By reducing to the lowest terms,
= 8
RHS :
= 8
LHS = RHS = 8
Hence verified
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)
Therefore y :
y = 7 - 3x
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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
= 7
= 7
= 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
= 8
= 8
= 8
= 8
LHS = RHS = 8
Hence verified
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TO FIND : x + y
substituting the values,