What is the solution of (x+y=5) and (2x+3y=12)?
Answer and explanation
Correct answer: x=3, y=2
The appropriate algebraic method is substitution. From the simpler equation x+y=5, isolate x to obtain x=5-y. Substitute this into the second equation: 2(5-y)+3y=12. Expanding gives 10-2y+3y=12, so y=2. Substituting y=2 into x=5-y gives x=3. Therefore the solution is (x,y)=(3,2), and option B is correct. Verification is important: 3+2=5 and 2(3)+3(2)=6+6=12, so both original equations hold. Option A reverses the two values and gives 2+3=5 but 2(2)+3(3)=13, so it fails the second equation. Options C and D also satisfy neither equation pair simultaneously. Thus only B is unambiguous.
Frequently asked questions
What is the correct answer to this question?
x=3, y=2
Why is this the correct answer?
The appropriate algebraic method is substitution. From the simpler equation x+y=5, isolate x to obtain x=5-y. Substitute this into the second equation: 2(5-y)+3y=12. Expanding gives 10-2y+3y=12, so y=2. Substituting y=2 into x=5-y gives x=3. Therefore the solution is (x,y)=(3,2), and option B is correct. Verification is important: 3+2=5 and 2(3)+3(2)=6+6=12, so both original equations hold. Option A reverses the two values and gives 2+3=5 but 2(2)+3(3)=13, so it fails the second equation. Options C and D also satisfy neither equation pair simultaneously. Thus only B is unambiguous.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Algebraic methods: Substitution method and Elimination method..
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