Which pair of equations will give a unique solution?
Answer and explanation
Correct answer: x + 3y = 10 and 3x + y = 10
For a pair a₁x+b₁y+c₁=0 and a₂x+b₂y+c₂=0, a unique solution occurs when a₁/a₂ is not equal to b₁/b₂. This means the two lines have different slopes and intersect at exactly one point. In option C, the coefficient ratios are 1/3 and 3/1, which are unequal, so the lines intersect uniquely. In option A, the second equation becomes the first divided by 2, so the lines coincide. In option B, the left side doubles but the constant does not, producing parallel distinct lines. In option D, the first equation is four times the second, so the lines coincide. Therefore C is the only correct choice.
Frequently asked questions
What is the correct answer to this question?
x + 3y = 10 and 3x + y = 10
Why is this the correct answer?
For a pair a₁x+b₁y+c₁=0 and a₂x+b₂y+c₂=0, a unique solution occurs when a₁/a₂ is not equal to b₁/b₂. This means the two lines have different slopes and intersect at exactly one point. In option C, the coefficient ratios are 1/3 and 3/1, which are unequal, so the lines intersect uniquely. In option A, the second equation becomes the first divided by 2, so the lines coincide. In option B, the left side doubles but the constant does not, producing parallel distinct lines. In option D, the first equation is four times the second, so the lines coincide. Therefore C is the only correct choice.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Conditions for solvability.
