What is the solution of x = 3y − 1 and x + y = 11?
Answer and explanation
Correct answer: x = 8, y = 3
The governing algebraic idea is substitution: when one variable is already expressed in terms of the other, replace it in the second equation. Since x = 3y − 1, substitute this expression into x + y = 11: (3y − 1) + y = 11. Combining like terms gives 4y − 1 = 11, so 4y = 12 and y = 3. Substituting y = 3 back into x = 3y − 1 gives x = 9 − 1 = 8. Thus the ordered solution is (8, 3), making option A correct. The other pairs fail either the first equation, the second equation, or both.
Frequently asked questions
What is the correct answer to this question?
x = 8, y = 3
Why is this the correct answer?
The governing algebraic idea is substitution: when one variable is already expressed in terms of the other, replace it in the second equation. Since x = 3y − 1, substitute this expression into x + y = 11: (3y − 1) + y = 11. Combining like terms gives 4y − 1 = 11, so 4y = 12 and y = 3. Substituting y = 3 back into x = 3y − 1 gives x = 9 − 1 = 8. Thus the ordered solution is (8, 3), making option A correct. The other pairs fail either the first equation, the second equation, or both.
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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