In which of the following pairs of linear equations will y be eliminated directly on adding the two equations, without multiplying either equation?
Answer and explanation
Correct answer: \(2x+3y=10,\; 5x-3y=4\)
In option A, the coefficients of y are 3 and -3. Therefore, on adding the equations, \(3y+(-3y)=0\), so y is eliminated. In option B, adding eliminates x instead, while in option C the y-coefficients are 4 and -2, so y does not cancel directly. Exam tip: For elimination by addition, look for equal coefficients with opposite signs for the variable to be removed.
Frequently asked questions
What is the correct answer to this question?
\(2x+3y=10,\; 5x-3y=4\)
Why is this the correct answer?
In option A, the coefficients of y are 3 and -3. Therefore, on adding the equations, \(3y+(-3y)=0\), so y is eliminated. In option B, adding eliminates x instead, while in option C the y-coefficients are 4 and -2, so y does not cancel directly. Exam tip: For elimination by addition, look for equal coefficients with opposite signs for the variable to be removed.
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..
