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
If both lines appear exactly at the same place on the graph, how many solutions will there be?If (a₁/a₂ ≠ b₁/b₂), how will two lines appear on the graph?How many solutions are there for (2x + 5y = 20) and (4x + 10y = 40)?Which pair of equations will give a unique solution?If a₁ = 4, b₁ = 6, c₁ = 10 and a₂ = 2, b₂ = 3, c₂ = 5, how will the lines be related?If a₁ = 6, b₁ = 9, c₁ = 12 and a₂ = 2, b₂ = 3, c₂ = 4, how will the lines be?If a₁ = 7, b₁ = 14, c₁ = 21 and a₂ = 1, b₂ = 2, c₂ = 3, how will the lines be?If the line \(3x+ay=24\) coincides with the line \(3x+4y=24\), what is the value of \(a\)?If the line \(4x+ay=20\) is coincident with the line \(2x+3y=10\), what is the value of \(a\)?What type of lines are 9x − 6y = 21 and 3x − 2y = 7?If 4x + 3y = p and 8x + 6y = 42 give infinitely many solutions, what is p?What type of lines are 12x + 15y = 30 and 4x + 5y = 10?If 5x + 4y = p and 15x + 12y = 96 give infinitely many solutions, what is p?Which statement is correct about 6x+4y=40 and 3x+2y=20?If 3x+6y=24 and x+2y=8, what is the number of solutions?What is the number of solutions of 5x−10y=15 and x−2y=3?What is the value of (p) for (2x+py=10) and (4x+6y=20) to have infinitely many solutions?If 7x−14y=28 and x−2y=4, which statement is correct?What is the value of (p) for (px-6y=18) and (2x-3y=9) to have infinitely many solutions?For (5x+10y=20) and (kx+2y=7) to have no solution, what is the value of (k)?