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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 the value of (p) for (px-8y=24) and (3x-4y=12) to have infinitely many solutions?What is the value of (a) for (ax+6y=14) and (2x+3y=7) to have infinitely many solutions?For (6x+12y=30) and (kx+2y=8) to have no solution, what is the value of (k)?What is the value of (p) for (px-10y=30) and (3x-5y=15) to have infinitely many solutions?For 12x + 18y = 54 and 2x + 3y = c to have no solution, which value of c is correct?What is the value of (a) for (ax+9y=27) and (2x+3y=9) to have infinitely many solutions?What is the number of solutions of 4x+7y=31 and 8x+14y=62?If two linear equations have (a_1/a_2 \ne b_1/b_2), how many solutions will they have?If (a_1/a_2=b_1/b_2 \ne c_1/c_2), what type of pair of equations is it?If a₁/a₂ = b₁/b₂ = c₁/c₂, how many solutions will the pair of linear equations have?Choose the correct statement for (2x+3y-5=0) and (4x+6y-10=0).What is the solution type of (x+y-4=0) and (2x+2y-9=0)?Find the number of solutions for (3x+2y-7=0) and (6x+5y-14=0).If two lines intersect at one point in a graph, how many solutions does the pair of equations have?If two lines are parallel in a graph, which option is correct for the pair of equations?If both lines become the same line in a graph, how many solutions will there be?Which conclusion is correct for (5x-y+2=0) and (10x-2y+3=0)?What type of pair are (7x+4y-8=0) and (14x+8y-16=0)?For (2x-5y+1=0) and (3x+y-4=0), what follows from comparing (a_1/a_2) and (b_1/b_2)?If (a_1/a_2=b_1/b_2=c_1/c_2), what will be the position of the lines?