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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

Which statement is correct by observing (8x+3y=17) and (16x+6y=34)?What is the correct conclusion by observing (9x-6y=12) and (3x-2y=7)?What is the correct solution status for (13x+2y=31) and (6x+y=14)?What is the correct solution status for (4x-3y=11) and (12x-9y=35)?What will be the value of (m) for (2x+my=14) and (8x+20y=56) to have infinitely many solutions?What conclusion follows from comparing the ratios of (a) and (b) in (7x+4y=18) and (3x+2y=10)?What is the value of (k) for (5x+4y=18) and (10x+8y=k) to have infinitely many solutions?What will (a) be for (3x+ay=21) and (9x+12y=63) to have infinitely many solutions?What value of (k) makes (kx+7y=28) and (8x+14y=60) have no solution?If (4x+5y=16) and (8x+10y=m) form an inconsistent pair, what is the correct condition for (m)?What is the correct conclusion for (7x+2y=19) and (14x+4y=38)?How many solutions will (6x-5y=14) and (12x-10y=31) have?What is the correct solution status for (4x+9y=25) and (8x+17y=49)?If (a_1/a_2=b_1/b_2=c_1/c_2), what will be the classification of the pair?If (a_1/a_2=b_1/b_2 \ne c_1/c_2), how will the lines appear in the graph?What will (p) be for (px+3y=15) and (12x+6y=30) to have infinitely many solutions?Which condition is correct for (3x+qy=11) and (7x+14y=26) to have a unique solution?What is the value of (k) for (5x+ky=35) and (x+4y=7) to have infinitely many solutions?What will (a) be for (8x+ay=40) and (2x+6y=13) to have no solution?Which statement is correct about the graph of (10x+15y=35) and (2x+3y=9)?