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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

For infinitely many solutions of ((m-1)x+6y=10) and (3x+9y=15), what is the value of (m)?When will the pair ((p+2)x+5y=11) and (6x+10y=13) have a unique solution?If (9x-3y=6) and ((q+3)x-qy=10) have no solution, what is (q)?What is the value of (r) for infinitely many solutions of (4x+(r-2)y=14) and (10x+15y=35)?Which condition gives a unique solution for (ax+7y=13) and (5x+by=9)?For infinitely many solutions of (6x-8y=16) and (sx-12y=24), what is (s)?For the pair (3x+4y=t) and (12x+16y=20) to have no solution, what condition is required on (t)?When will (11x+2y=3) and (22x+ny=8) have a unique solution?What type of solution is given by the lines 2x − 5y = 1 and 6x − 15y = 3?What is the correct conclusion for the lines (7x+3y=10) and (14x+6y=19)?What is the solution status of 4x-7y=5 and 12x-21y=17?Which statement is correct for the pair 2x + 3y = 5 and 4x + 6y = 10?What is the nature of the pair (9x-4y=11) and (18x-8y=21)?If two linear equations are \(a_1x+b_1y+c_1=0\) and \(a_2x+b_2y+c_2=0\), when do they have infinitely many solutions?For no solution in (k+1)x+4y=9 and 6x+8y=15, what is k?Find m for infinitely many solutions of 7x + (m − 4)y = 13 and 14x + 6y = 26.When will ((p-2)x+9y=4) and (5x+15y=12) have a unique solution?For infinitely many solutions of (3x+ay=6) and (9x+12y=b), what is ((a,b))?For no solution in (5x-2y=c) and (15x-6y=21), what condition should (c) satisfy?When will (rx+5y=2) and (8x+10y=4) have a unique solution?