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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

What is the most suitable conclusion by observing (6x+7y=41) and (18x+21y=123)?Which conclusion is correct by observing (12x+16y=36) and (3x+4y=11)?What is found by comparing the ratios of (a) and (b) in (11x+6y=35) and (5x+3y=17)?What type of pair is 16x+24y=88 and 2x+3y=11?What type of pair is (18x+27y=63) and (2x+3y=8)?What type of pair is (13x+4y=39) and (6x+2y=17)?In a shop the equations for two items are (3x+4y=150) and (9x+12y=450). How many solutions will there be?For prices of two tickets the equations (5x+4y=180) and (10x+8y=370) are formed. What type of system is this?For two numbers the equations (4x+y=19) and (x-3y=2) are formed. What will be the solution status?What is the relation among all three ratios in (5x+6y=32) and (15x+18y=96)?Which of the following pairs of equations will have coincident lines as their graphs?Which statement is correct for (7x+8y=26) and (14x+15y=51)?What should (s) be for (4x+5y=29) and (8x+10y=s) to be consistent and dependent?Which condition is correct for (6x+7y=31) and (12x+14y=r) to be inconsistent?Which condition indicates that a pair of linear equations in two variables has infinitely many solutions?What will (k) be for (8x+ky=72) and (2x+7y=18) to have infinitely many solutions?If (lx+11y=44) and (10x+22y=91) have no solution then what will be the value of (l)?Which statement is correct by observing (12x+5y=41) and (24x+10y=82)?What is the correct conclusion by observing (14x-10y=36) and (7x-5y=19)?What is the correct solution status for (17x+6y=52) and (8x+3y=25)?