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
How many solutions will the equations (8x+3y=19) and (16x+6y=45) have?What is the correct solution status for the equations (5x+11y=32) and (9x+20y=58)?If (a_1/a_2 \ne b_1/b_2), what will be the correct nature of the pair?If (a_1/a_2=b_1/b_2 \ne c_1/c_2), which graphical conclusion is correct?What will (k) be for the equations (kx+10y=30) and (12x+15y=45) to have infinitely many solutions?What is the value of (q) for the equations (9x+qy=36) and (18x+14y=72) to have infinitely many solutions?Which condition is correct for the equations (8x+py=40) and (2x+3y=11) to have a unique solution?What will (a) be for the equations (7x+ay=49) and (21x+18y=147) to have infinitely many solutions?What is the value of (b) for the equations (bx+12y=48) and (10x+30y=101) to have no solution?Which statement is correct about the graph of the equations (18x+24y=54) and (3x+4y=11)?What will be shown in the graph of the equations (20x+15y=85) and (4x+3y=17)?What is the correct description of the graph of the equations (3x+13y=41) and (8x+29y=91)?If two lines have the same slope and the same (y)-intercept, what will be the solutions of the pair?If two lines have the same slope but different (y)-intercepts, what will be the nature of the pair?If two lines have different slopes, which statement is correct?Which ratio relation is correct for the equations (6x+11y-47=0) and (18x+33y-141=0)?What is the correct ratio relation for the equations (10x-7y+31=0) and (20x-14y+65=0)?What is the correct conclusion for the equations (11x+4y-29=0) and (22x+9y-58=0)?If (cx+14y=56) and (15x+35y=121) have no solution, what will (c) be?What is the value of (d) for the equations (5x+dy=40) and (20x+28y=160) to have infinitely many solutions?