Which pair of equations will give a unique solution on the graph?
Answer and explanation
Correct answer: x + 2y = 7 and 2x + y = 8
A pair has a unique graphical solution when its two lines intersect at exactly one point. For option C, the coefficient ratios are a₁/a₂ = 1/2 and b₁/b₂ = 2/1 = 2, which are unequal. Therefore the lines have different slopes and must meet once. In option A, the second equation is half the first, so the lines coincide. In option B, the left sides are proportional but the constants are not, giving distinct parallel lines and no solution. In option D, the first equation is three times the second, so the lines coincide. Hence option C is correct.
Frequently asked questions
What is the correct answer to this question?
x + 2y = 7 and 2x + y = 8
Why is this the correct answer?
A pair has a unique graphical solution when its two lines intersect at exactly one point. For option C, the coefficient ratios are a₁/a₂ = 1/2 and b₁/b₂ = 2/1 = 2, which are unequal. Therefore the lines have different slopes and must meet once. In option A, the second equation is half the first, so the lines coincide. In option B, the left sides are proportional but the constants are not, giving distinct parallel lines and no solution. In option D, the first equation is three times the second, so the lines coincide. Hence option C is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Graphical method of finding solutions..
