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 condition is correct for (8x+py=24) and (2x+3y=7) to have a unique solution?If (5x+2y=16) and (10x+4y=n) have infinitely many solutions, what is (n)?If 6x − 2y = 18 and 3x − y = t are inconsistent, what is the correct condition for t?What is the most suitable conclusion by observing (3x+2y=8) and (9x+6y=24)?Which conclusion is correct by observing (4x+8y=12) and (x+2y=5)?What is found by comparing the ratios of (a) and (b) in (7x+3y=19) and (2x+y=6)?What type of pair is 12x+18y=30 and 2x+3y=5?What type of pair is (10x+15y=25) and (2x+3y=8)?What type of pair is (11x+4y=18) and (5x+2y=9)?For two items in a shop, the equations are (x+2y=50) and (2x+4y=100). How many solutions will there be?Which condition ensures that the pair of linear equations \(a_1x+b_1y+c_1=0\) and \(a_2x+b_2y+c_2=0\) has infinitely many solutions?If the equations for two numbers are (x+y=12) and (2x-y=3), what will be the solution status?For (2x+3y=13) and (4x+6y=26), what is the relation among (a_1/a_2), (b_1/b_2), and the constant ratio?Which relation is correct for (6x+9y=30) and (2x+3y=12)?Which statement is correct for (7x+5y=16) and (14x+11y=35)?What should (s) be for (x+4y=9) and (2x+8y=s) to be consistent and dependent?Which condition is correct for (3x+5y=14) and (6x+10y=r) to be inconsistent?What will (a) be for (2x+3y=5) and (4x+ay=11) to have no solution?What will (k) be for (5x+ky=25) and (x+3y=5) to have infinitely many solutions?If (lx+7y=21) and (6x+14y=40) have no solution, what will be the value of (l)?