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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

How many solutions will (9x-4y=17) and (18x-8y=39) have?What is the correct solution status for (4x+7y=23) and (9x+15y=48)?If (a_1/a_2=b_1/b_2=c_1/c_2) then what will be the nature of the pair of equations?If (a_1/a_2=b_1/b_2 \ne c_1/c_2) then which situation will occur in the graph?What is the value of (p) for (px+6y=18) and (10x+15y=45) to have infinitely many solutions?What will (q) be for (7x+qy=29) and (14x+10y=58) to have infinitely many solutions?Which condition is correct for (6x+ky=24) and (3x+5y=17) to have a unique solution?What will (a) be for (5x+ay=35) and (15x+18y=105) to have infinitely many solutions?What will (b) be for (bx+8y=32) and (12x+24y=71) to have no solution?Which statement is correct about the graph of (14x+21y=49) and (2x+3y=8)?What will be shown in the graph of (15x+10y=40) and (3x+2y=8)?What is the correct description of the graph of (2x+11y=27) and (5x+19y=46)?Which ratio relation is correct for (4x+9y-31=0) and (12x+27y-93=0)?What is the correct ratio relation for (8x-3y+22=0) and (16x-6y+47=0)?What is the correct conclusion for (9x+5y-28=0) and (18x+11y-56=0)?If (ax+9y=27) and (14x+21y=64) have no solution then what will (a) be?What is the value of (b) for (3x+by=24) and (12x+20y=96) to have infinitely many solutions?Which condition is correct for (11x+py=33) and (4x+2y=15) to have a unique solution?If (7x+4y=37) and (21x+12y=n) have infinitely many solutions then what is (n)?If 10x − 5y = 30 and 2x − y = t are inconsistent, what is the correct condition on t?