Mathematics
Conditions for solvability
युग्म रैखिक समीकरणों के हल की शर्तें
In this Class 10 Mathematics topic, students learn how to determine whether a pair of linear equations in two variables has a solution. They compare the ratios of the coefficients and constants to identify the three possibilities: a unique solution, infinitely many solutions, or no solution. The topic connects algebraic conditions with the graphical meaning of intersecting, coincident, and parallel lines, helping students classify equation pairs accurately and understand when they are consistent or inconsistent.
Practice questions
Which of the following pairs is inconsistent?Which of the following pairs is consistent and dependent?What is the quickest conclusion by observing (2x+3y=5) and (4x+6y=10)?Which conclusion is correct by observing (3x+6y=12) and (x+2y=5)?What is found by comparing the first two ratios in (4x+y=9) and (7x+2y=13)?If two lines have different slopes then which statement about the pair is correct?If two lines have the same slope and the same intercept then what kind of lines will they be?What kind of pair is (13x+5y=22) and (26x+10y=45)?What is the correct solution status for (4x-7y=3) and (8x-13y=6)?Choose the correct statement for (15x+10y=5) and (3x+2y=1).Which conclusion is correct for (16x-8y=24) and (2x-y=4)?Which option is correct for (6x+11y=7) and (3x+5y=4)?If two equations satisfy a₁/a₂ = b₁/b₂ and this common ratio is also equal to c₁/c₂, what happens?If two equations have (a₁/a₂=b₁/b₂) but (c₁/c₂) is different then what happens?State the correct solution status for \(17x+4y=29\) and \(9x+2y=16\).What is the correct conclusion for (18x+6y=12) and (3x+y=2)?What will be the number of solutions for (5x+10y=25) and (x+2y=6)?If the equations (4x+6y=18) and (2x+3y=k) have infinitely many solutions, what is the value of (k)?What is the value of a for the pair of equations 3x + ay = 12 and 6x + 8y = 24 to have infinitely many solutions?What should (k) be for (kx+5y=20) and (6x+10y=45) to have no solution?