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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

If (2x+3y=7) and (4x+6y=m) form an inconsistent pair, what is the correct condition for (m)?Which conclusion is correct for (5x+2y=11) and (10x+4y=22)?How many solutions will (7x-3y=10) and (14x-6y=25) have?Choose the correct option for (3x+4y=13) and (6x+7y=25).If (a_1/a_2=b_1/b_2=c_1/c_2), what will be the position of both lines in the graph?If (a_1/a_2=b_1/b_2 \ne c_1/c_2), which statement about the pair is correct?What is the value of (p) for (px+2y=6) and (9x+6y=18) to have infinitely many solutions?Which condition is correct for (2x+qy=8) and (5x+10y=21) to have a unique solution?What will (k) be for (4x+ky=16) and (x+3y=4) to have infinitely many solutions?What is the value of (a) for (6x+ay=30) and (2x+5y=11) to have no solution?Choose the correct statement about the graph of (8x+12y=20) and (2x+3y=6).What will be shown in the graph of (9x+6y=15) and (3x+2y=5)?If two lines have the same slope and the same (y)-intercept, what will be the type of pair?If two lines have the same slope but different y-intercepts, which conclusion is correct?If two lines have different slopes, what will be the solution status of the pair?Which ratio relation is correct for (2x+3y-11=0) and (6x+9y-33=0)?What is the correct ratio relation for 4x − 5y + 7 = 0 and 8x − 10y + 9 = 0?What is the correct conclusion for (5x+6y-4=0) and (10x+9y-8=0)?If the equations (ax+4y=10) and (6x+8y=25) have no solution, what is the value of (a)?What will (b) be for (3x+by=15) and (9x+12y=45) to have infinitely many solutions?