Solving (2(x-1)+3(y+2)=25) and (4(x-1)-3(y+2)=5), what is (x+y)?
Answer and explanation
Correct answer: (9)
Let u=x-1 and v=y+2. The equations become 2u+3v=25 and 4u-3v=5. Adding them eliminates v and gives 6u=30, so u=5. Substituting into the first equation gives 10+3v=25, hence v=5. Therefore, x=6 and y=3, so x+y=9; option B is correct. Exam tip: when the coefficients of one variable have opposite signs, add the equations to eliminate that variable directly.
Frequently asked questions
What is the correct answer to this question?
(9)
Why is this the correct answer?
Let u=x-1 and v=y+2. The equations become 2u+3v=25 and 4u-3v=5. Adding them eliminates v and gives 6u=30, so u=5. Substituting into the first equation gives 10+3v=25, hence v=5. Therefore, x=6 and y=3, so x+y=9; option B is correct. Exam tip: when the coefficients of one variable have opposite signs, add the equations to eliminate that variable directly.
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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