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 will be shown in the graph of the equations (15x+10y=40) and (3x+2y=8)?What is the correct description of the graph of the equations (2x+11y=27) and (5x+19y=46)?Which ratio relation is correct for the equations (4x+9y-31=0) and (12x+27y-93=0)?What is the correct ratio relation for the equations (8x-3y+22=0) and (16x-6y+47=0)?What is the correct conclusion for the equations (9x+5y-28=0) and (18x+11y-56=0)?What is the value of (b) for the equations (3x+by=24) and (12x+20y=96) to have infinitely many solutions?Which condition is correct for the equations (11x+py=33) and (4x+2y=15) to have a unique solution?What is the most suitable conclusion by observing the equations (6x+7y=41) and (18x+21y=123)?Which conclusion is correct by observing the equations (12x+16y=36) and (3x+4y=11)?What is found by comparing the ratios of (a) and (b) in the equations (11x+6y=35) and (5x+3y=17)?What type of pair is formed by 16x+24y=88 and 2x+3y=11?What type of pair is formed by the equations (18x+27y=63) and (2x+3y=8)?What type of pair is formed by the equations (13x+4y=39) and (6x+2y=17)?What is the relation among all three ratios in the equations (5x+6y=32) and (15x+18y=96)?Which relation is correct for the equations (10x+15y=50) and (2x+3y=13)?Which statement is correct for the equations (7x+8y=26) and (14x+15y=51)?What should (s) be for the equations (4x+5y=29) and (8x+10y=s) to be consistent and dependent?Which condition is correct for the equations (6x+7y=31) and (12x+14y=r) to be inconsistent?A student claims that the equations \(3x-2y=5\) and \(6x-4y=12\) have infinitely many solutions because the ratios of the coefficients of \(x\) and \(y\) are equal. Considering the student's error, which conclusion is correct?What will (k) be for the equations (8x+ky=72) and (2x+7y=18) to have infinitely many solutions?