What is the solution of (0.5x-y=1.5) and (x+0.25y=7)?
Answer and explanation
Correct answer: (x=59/9, y=16/9)
Multiplying the first equation by 2 and the second by 4 removes the decimals, giving x-2y=3 and 4x+y=28. Multiply the first of these by 2 and add it to the second equation: 9x=59, so x=59/9. Substituting this into x-2y=3 gives y=16/9. Therefore, the solution is (59/9, 16/9). For example, option B satisfies the first equation, but in the second equation it gives 6+0.25(3/2)=6.375, not 7. Exam tip: When coefficients are decimals, first convert the equations to integer coefficients and then verify the final pair in both original equations.
Frequently asked questions
What is the correct answer to this question?
(x=59/9, y=16/9)
Why is this the correct answer?
Multiplying the first equation by 2 and the second by 4 removes the decimals, giving x-2y=3 and 4x+y=28. Multiply the first of these by 2 and add it to the second equation: 9x=59, so x=59/9. Substituting this into x-2y=3 gives y=16/9. Therefore, the solution is (59/9, 16/9). For example, option B satisfies the first equation, but in the second equation it gives 6+0.25(3/2)=6.375, not 7. Exam tip: When coefficients are decimals, first convert the equations to integer coefficients and then verify the final pair in both original equations.
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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