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
For (3x-2y=5) and (12x-8y=c) to have no solution, what condition is required on (c)?When will qx + 4y = 9 and 15x + 10y = 18 have a unique solution?For infinitely many solutions of 5x + (r + 1)y = 11 and 15x + 18y = 33, what is r?What is the value of (n) for no solution in (2x+ny=7) and (6x+15y=19)?When will (11x+3y=4) and (22x+sy=10) have a unique solution?What is the value of (t) for infinitely many solutions of (6x-ty=18) and (14x-21y=42)?What type of pair is formed by the lines (7x+2y=9) and (21x+6y=25)?What is the correct conclusion for the lines (9x-5y=13) and (18x-10y=26)?How many solutions will the pair (10x+3y=17) and (20x+9y=31) have?What is the solution status of (4x+9y=2) and (8x+18y=7)?Choose the correct option for (13x+4y=6) and (26x+8y=12).What is the number of solutions of 12x - 7y = 5 and 18x - 11y = 8?For infinitely many solutions of (u + 3)x + 8y = 16 and 10x + 20y = 40, what is u?What is the value of (v) for no solution in (5x+(v-2)y=3) and (15x+9y=14)?When will (wx-6y=4) and (16x-24y=12) have a unique solution?For infinitely many solutions of (3x+2y=\lambda) and (18x+12y=48), what is (\lambda)?What is (\mu) for no solution in (14x+\mu y=9) and (21x+6y=20)?When will (α - 1)x + 5y = 2 and 8x + 10y = 6 have a unique solution?For infinitely many solutions of (9x+(\beta+4)y=15) and (27x+18y=45), what is (\beta)?What is the value of (\gamma) for no solution in (5x+\gamma y=1) and (25x+15y=11)?