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 statement is correct by observing the equations (12x+5y=41) and (24x+10y=82)?What is the correct conclusion by observing the equations (14x-10y=36) and (7x-5y=19)?What is the correct solution status for the equations (17x+6y=52) and (8x+3y=25)?What is the correct condition on (s) for the equations (4x+9y=26) and (12x+27y=s) to be inconsistent?What will be the value of (m) for the equations (mx+5y=15) and (18x+15y=45) to have infinitely many solutions?What will (a) be for the equations (7x+ay=20) and (14x+10y=47) to have no solution?Which condition is correct for the equations (2x+3y=8) and (5x+ky=19) to have a unique solution?What is the correct solution status for the equations (6x-4y+11=0) and (15x-10y+28=0)?What will be the graph of the equations (3x+8y=27) and (9x+24y=81)?What type of pair is formed by 11x + 7y = 30 and 4x + 3y = 12?For prices of two items, the equations (6x+5y=240) and (12x+10y=490) are formed. What type of system is this?If a pair of linear equations is written as \(a_1x+b_1y+c_1=0\) and \(a_2x+b_2y+c_2=0\), under which condition will it have a unique solution?What is the relation among all three ratios in the equations (8x+12y=40) and (2x+3y=10)?What is the correct conclusion by observing the equations (16x-12y=44) and (4x-3y=12)?Which statement is correct for the equations (9x+2y=25) and (18x+5y=54)?What is the value of (c) for the equations (cx+10y=50) and (9x+15y=80) to have no solution?What is the value of (a) for the equations (4x+ay=28) and (12x+15y=84) to have infinitely many solutions?What is the value of (p) for the equations (px+6y=18) and (14x+21y=50) to have no solution?If (3x+8y=25) and (9x+24y=m) form an inconsistent pair, what is the correct condition for (m)?Which conclusion is correct for the equations 6x − 5y = 17 and 18x − 15y = 51?