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Subjects

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

If the graphs of the two linear equations \(a_1x+b_1y+c_1=0\) and \(a_2x+b_2y+c_2=0\) are coincident lines, which condition correctly shows that they have infinitely many solutions?If (8x+5y=43) and (24x+15y=n) have infinitely many solutions, what is (n)?If 12x − 6y = 42 and 2x − y = t are inconsistent, what is the correct condition on t?What is the most suitable conclusion by observing the equations (7x+12y=53) and (21x+36y=159)?Which conclusion is correct by observing the equations (15x+20y=55) and (3x+4y=12)?What is found by comparing the ratios of (a) and (b) in the equations (13x+8y=47) and (6x+4y=23)?What type of pair is formed by 18x+30y=126 and 3x+5y=21?What type of pair is formed by the equations (20x+28y=84) and (5x+7y=23)?What type of pair is formed by the equations (14x+5y=44) and (7x+3y=23)?In a shop, the equations for two items are (4x+7y=210) and (12x+21y=630). How many solutions will there be?For prices of two tickets, the equations (7x+5y=260) and (14x+10y=535) are formed. What type of system is this?For two numbers, the equations (5x+2y=31) and (2x-3y=4) are formed. What will be the solution status?What is the relation among all three ratios in the equations (7x+10y=46) and (21x+30y=138)?If the graphs of two linear equations are coincident lines, which condition on the ratios of their coefficients is correct?Which statement is correct for the equations (8x+9y=37) and (16x+17y=73)?What should (s) be for the equations (6x+11y=53) and (18x+33y=s) to be consistent and dependent?Which condition is correct for the equations (9x+4y=31) and (18x+8y=r) to be inconsistent?How do the lines appear on a graph when a pair of linear equations in two variables has infinitely many solutions?What will (k) be for the equations (9x+ky=81) and (3x+8y=27) to have infinitely many solutions?If (lx+13y=52) and (14x+26y=109) have no solution, what will be the value of (l)?