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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 the general pair (a_1x+b_1y+c_1=0) and (a_2x+b_2y+c_2=0), what is the condition for a unique solution?If \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\), what is the solution status of the pair?If two lines have the same slope and the same intercept, how many solutions will their pair of equations have?If two lines are distinct and parallel, what is the correct ratio condition?If (a_1b_2-a_2b_1\neq0), what is the correct statement about the pair?If (D=0), (D_x=0), and (D_y=0), what happens in a pair of two linear equations?For ((z+2)x+3y=5) and (6x+(z-1)y=7) to be non-unique, what are the possible values of (z)?What is the condition for a unique solution of (ax+2y=3) and (4x+ay=9)?What is the value of b for infinitely many solutions of 2x + by = 6 and bx + 8y = 24?What is (c) for no solution in (cx+6y=5) and (9x+18y=10)?What is the value of d for infinitely many solutions of 4x + dy = 7 and 12x + 15y = 21?When will (ex-4y=9) and (18x-12y=27) have a unique solution?What is (f) for no solution in (7x+fy=2) and (28x+20y=13)?For infinitely many solutions of ((g-1)x+10y=15) and (8x+20y=30), what is (g)?When will (hx+12y=6) and (10x+15y=20) have a unique solution?What is the value of (i) for no solution in (6x+iy=12) and (18x+27y=50)?For infinitely many solutions of (jx+5y=10) and (14x+7y=14), what is (j)?What is the value of k for no solution in 2x + 3y = 4 and kx + 6y = 11?When will (mx+7y=13) and (16x+14y=26) have a unique solution?For infinitely many solutions of 3x + ny = 18 and 5x + 10y = 30, what is n?