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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 correct conclusion for (8x+12y=24) and (2x+3y=7)?State the correct solution status for (9x+5y=17) and (4x+2y=11).In which condition is a pair of two linear equations called consistent and independent?In which condition is a pair of two linear equations called consistent and dependent?What will be the number of solutions for (x-3y=4) and (2x-6y=9)?Which option is correct for (3x-2y=6) and (12x-8y=24)?Choose the correct conclusion for (11x+6y=19) and (5x+3y=8).What is the value of (a) for (2x+ay=5) and (6x+9y=15) to have infinitely many solutions?What will (k) be for (kx+4y=8) and (3x+2y=9) to have no solution?What is the value of (b) for (5x+by=20) and (10x+6y=40) to have infinitely many solutions?What is the value of (p) for (px+5y=10) and (4x+10y=23) to have no solution?What will (m) be for infinitely many solutions of (7x+my=28) and (x+2y=4)?What is the condition for the pair of linear equations \(a_1x+b_1y+c_1=0\) and \(a_2x+b_2y+c_2=0\) to have infinitely many solutions?Which condition is correct for (qx+6y=18) and (5x+3y=12) to have a unique solution?What will (k) be for (2x+3y=9) and (4x+ky=18) to have infinitely many solutions?What should (t) not be for (3x+2y=11) and (6x+4y=t) to have no solution?What will be the graph of (x+2y=6) and (3x+6y=18)?What will be the graph of (2x+4y=10) and (x+2y=7)?What will the graph of (5x+8y=15) and (3x+4y=9) show?Which of the following pairs is consistent and independent?