If y = x − 2 and 2x + y = 13, which is the correct solution?
Answer and explanation
Correct answer: x = 5, y = 3
The governing concept is substitution. Since y is already isolated as y = x − 2, replace y in the second equation: 2x + (x − 2) = 13. Combining like terms gives 3x − 2 = 13; adding 2 gives 3x = 15, and therefore x = 5. Now substitute x = 5 into y = x − 2: y = 5 − 2 = 3. Thus the solution is (x, y) = (5, 3), so option A is correct. Verification gives 2(5) + 3 = 13. Each other option fails either the relation y = x − 2 or the second equation.
Frequently asked questions
What is the correct answer to this question?
x = 5, y = 3
Why is this the correct answer?
The governing concept is substitution. Since y is already isolated as y = x − 2, replace y in the second equation: 2x + (x − 2) = 13. Combining like terms gives 3x − 2 = 13; adding 2 gives 3x = 15, and therefore x = 5. Now substitute x = 5 into y = x − 2: y = 5 − 2 = 3. Thus the solution is (x, y) = (5, 3), so option A is correct. Verification gives 2(5) + 3 = 13. Each other option fails either the relation y = x − 2 or the second equation.
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..
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
