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The pair of linear equations x + y = 3, 2x + 5y = 12 has a unique solution x = x1, y = y1 then value of x1 is –
- a)1
- b)2
- c)-1
- d)-2
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The pair of linear equations x + y = 3, 2x + 5y = 12 has a unique solu...
The given system of equations is :x + y = 3 ..
(1)2x + 5y = 12 ..
(2)Now, multiply (1) by 2, we get2x + 2y = 6..
(3)Subtracting (3) from (2),
we get5y−2y = 12−6⇒3y = 6⇒y = 2
Put the value of y in (1),
we get
x + 2 = 3⇒x = 1
So, x1 = 1 and y1 = 2
This question is part of UPSC exam. View all Class 10 courses
Most Upvoted Answer
The pair of linear equations x + y = 3, 2x + 5y = 12 has a unique solu...
To find the value of x1, we need to solve the system of equations.
The first equation is x + y = 3.
Rearranging this equation, we get x = 3 - y.
Substituting this expression for x into the second equation, we have:
2(3 - y) + 5y = 12.
Expanding and simplifying, we get:
6 - 2y + 5y = 12.
Combining like terms, we have:
3y + 6 = 12.
Subtracting 6 from both sides, we get:
3y = 6.
Dividing both sides by 3, we find:
y = 2.
Substituting this value of y back into the first equation, we have:
x + 2 = 3.
Subtracting 2 from both sides, we find:
x = 1.
Therefore, the unique solution to the system of equations is x = 1, y = 2.
So, the value of x1 is 1.
The first equation is x + y = 3.
Rearranging this equation, we get x = 3 - y.
Substituting this expression for x into the second equation, we have:
2(3 - y) + 5y = 12.
Expanding and simplifying, we get:
6 - 2y + 5y = 12.
Combining like terms, we have:
3y + 6 = 12.
Subtracting 6 from both sides, we get:
3y = 6.
Dividing both sides by 3, we find:
y = 2.
Substituting this value of y back into the first equation, we have:
x + 2 = 3.
Subtracting 2 from both sides, we find:
x = 1.
Therefore, the unique solution to the system of equations is x = 1, y = 2.
So, the value of x1 is 1.
Community Answer
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The pair of linear equations x + y = 3, 2x + 5y = 12 has a unique solution x = x1, y = y1then value of x1is –a)1b)2c)-1d)-2Correct answer is option 'A'. Can you explain this answer?
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