Which is the solution of (x+2y=11) and (x+y=7)?
Answer and explanation
Correct answer: ( (3,4) )
The common solution must satisfy both equations simultaneously. A useful algebraic method is to compare the two equations and remove the common term x. The equations are x+2y=11 and x+y=7. Subtracting the second equation from the first gives y=4. Substituting this value into x+y=7 gives x+4=7, so x=3.
Hence the ordered pair is (3,4), which is option A. A direct check confirms it: in the first equation, 3+2(4)=3+8=11; in the second, 3+4=7. Thus the point (3,4) lies on both lines and is their intersection. The order matters: (4,3) would give 4+2(3)=10, not 11, so it cannot be the solution.
Frequently asked questions
What is the correct answer to this question?
( (3,4) )
Why is this the correct answer?
The common solution must satisfy both equations simultaneously. A useful algebraic method is to compare the two equations and remove the common term x. The equations are x+2y=11 and x+y=7. Subtracting the second equation from the first gives y=4. Substituting this value into x+y=7 gives x+4=7, so x=3.
Hence the ordered pair is (3,4), which is option A. A direct check confirms it: in the first equation, 3+2(4)=3+8=11; in the second, 3+4=7. Thus the point (3,4) lies on both lines and is their intersection. The order matters: (4,3) would give 4+2(3)=10, not 11, so it cannot be the solution.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Graphical method of finding solutions..
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