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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 condition on (t) for (3x+4y=22) and (9x+12y=t) to be inconsistent?What will be the value of (a) for (4x+ay=36) and (12x+21y=108) to have infinitely many solutions?Which condition is correct for (5x+2y=18) and (15x+ky=54) to have a unique solution?What is the correct solution status for (6x-7y+13=0) and (18x-21y+40=0)?For the prices of two items, the equations 2x + 7y = 160 and 5x + 16y = 370 are formed. What is the solution status?Which statement is correct about the graph of (7x+9y=43) and (14x+18y=86)?What is the value of (k) for the equations (3x+ky=12) and (9x+15y=36) to have infinitely many solutions?What is the value of (a) for the equations (ax+4y=10) and (6x+8y=25) to have no solution?If (2x+5y=17) and (4x+10y=m) form an inconsistent pair, what is the correct condition for (m)?Which conclusion is correct for the equations 5x − 3y = 11 and 10x − 6y = 22?How many solutions will the equations (7x+4y=19) and (14x+8y=41) have?What is the correct solution status for the equations (4x+7y=23) and (9x+15y=49)?If (a_1/a_2=b_1/b_2=c_1/c_2), what is the correct nature of the pair?If (a_1/a_2=b_1/b_2 \ne c_1/c_2), which situation will occur in the graph?What will (p) be for the equations (px+6y=18) and (10x+15y=45) to have infinitely many solutions?What is the value of (q) for the equations (7x+qy=29) and (14x+10y=58) to have infinitely many solutions?Which condition is correct for the equations (6x+ky=24) and (3x+5y=17) to have a unique solution?What will (a) be for the equations (5x+ay=35) and (15x+18y=105) to have infinitely many solutions?What is the value of (b) for the equations (bx+8y=32) and (12x+24y=71) to have no solution?Which statement is correct about the graph of the equations (14x+21y=49) and (2x+3y=8)?