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 two numbers, the equations (3x+y=14) and (x-2y=1) are formed. What will be the solution status?What is the relation among all three ratios in (3x+4y=22) and (6x+8y=44)?Which relation is correct for (8x+12y=40) and (2x+3y=12)?Which statement is correct for (6x+7y=23) and (12x+13y=45)?What should (s) be for (2x+5y=17) and (4x+10y=s) to be consistent and dependent?Which condition is correct for (5x+6y=29) and (10x+12y=r) to be inconsistent?What will (a) be for (3x+4y=10) and (6x+ay=25) to have no solution?What will (k) be for (6x+ky=42) and (2x+5y=14) to have infinitely many solutions?If (lx+9y=27) and (8x+18y=55) have no solution, what will be the value of (l)?Which statement is correct by observing (9x+2y=31) and (18x+4y=62)?What is the correct conclusion by observing (12x-8y=20) and (3x-2y=6)?What is the correct solution status for (15x+4y=37) and (7x+2y=18)?What will be the value of (m) for (3x+my=24) and (12x+28y=96) to have infinitely many solutions?What is the correct solution status for (11x-4y=26) and (22x-8y=53)?What conclusion follows from comparing the ratios of (a) and (b) in (5x+7y=32) and (9x+13y=58)?For prices of two items, the equations (4x+3y=125) and (8x+6y=260) are formed. What type of system is this?What is the value of (k) for (2x+5y=16) and (6x+15y=k) to have infinitely many solutions?What is the value of (a) for (ax+4y=20) and (9x+12y=61) to have no solution?If (5x+2y=13) and (10x+4y=m) form an inconsistent pair then what is the correct condition for (m)?What is the correct conclusion for (8x+3y=21) and (16x+6y=42)?