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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 s for infinitely many solutions of 12x + sy = 18 and 20x + 10y = 30?For no solution in (ux+9y=7) and (4x+6y=11), what is the value of (u)?When will (13x-ty=5) and (26x-10y=14) have a unique solution?For infinitely many solutions of ((v+2)x-3y=6) and (10x-5y=10), what is (v)?For (2x+3y=d) and (14x+21y=28) to have no solution, what condition is required on (d)?What is the condition for a unique solution of (ax+by=1) and (2ax+3by=5)?What is (l) for no solution in (lx+6y=8) and (9x+18y=10)?For infinitely many solutions of (6x+(h+1)y=12) and (15x+20y=30), what is (h)?Which solution status is correct for (x+2y=3) and (4x+8y=12)?Choose the correct statement about 3x − y = 4 and 6x − 2y = 9.How many solutions does (4x+5y=1) and (8x+9y=2) have?For the general pair (a_1x+b_1y+c_1=0) and (a_2x+b_2y+c_2=0), what is the condition for no solution?If coefficient ratios are equal and the constant ratio is different in a pair, what is the solution status?If (\frac{a_1}{a_2}\neq\frac{b_1}{b_2}), what is the conclusion for a pair of two linear equations?Which algebraic condition is correct for coincident lines?If D = 0 and at least one auxiliary determinant is non-zero, what is the solution status of the pair?If two lines have the same slope and different (y)-intercepts, how many solutions will their pair of equations have?If two lines have different slopes, which conclusion is correct for their pair?For ((k-3)x+2y=5) and (4x+ky=11) to be non-unique, what can (k) be?For no solution in ((k+1)x+6y=3) and (2x+12y=8), what is (k)?