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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 m for infinitely many solutions of 4x + (m − 5)y = 9 and 12x + 6y = 27?When will ((p+4)x-9y=2) and (5x-15y=6) have a unique solution?For no solution in (1/2)x + qy = 3 and 2x + 8y = 5, what is q?What is \(r\) for infinitely many solutions of \(rx+\frac{3}{2}y=6\) and \(8x+6y=24\)?When will (\alpha x+4y=7) and (9x+12y=21) have a unique solution?For no solution in (3x+(\beta-1)y=10) and (6x+4y=18), what is (\beta)?What is (\gamma) for infinitely many solutions of (5x-2y=\gamma) and (20x-8y=36)?Which condition gives a unique solution for ((s+2)x+3y=1) and (5x+(s-1)y=4)?What is the correct condition on (t) for the equations (5x+9y=64) and (15x+27y=t) to be inconsistent?What is the value of (a) for the equations (6x+ay=42) and (18x+33y=126) to have infinitely many solutions?What is the value of (p) for the equations (px+10y=50) and (14x+35y=122) to have no solution?Which condition is correct for the equations (11x+ky=70) and (5x+4y=31) to have a unique solution?What is the correct solution status for the equations (12x-7y+29=0) and (36x-21y+91=0)?What conclusion follows from comparing the ratios of a and b in 7x + 19y = 86 and 13x + 35y = 158?For prices of two items, the equations (10x+3y=470) and (20x+6y=955) are formed. What type of system is this?Which statement is correct by observing the equations (21x+8y=97) and (42x+16y=194)?When will the pair (kx+5y=10) and (6x+15y=18) have a unique solution?What is the value of (m) for no solution in (4x+my=8) and (10x+15y=21)?For infinitely many solutions of ((p-2)x+7y=14) and (9x+21y=42), what is (p)?Find the value of (a) for infinitely many solutions of (8x+ay=12) and (20x+10y=30).