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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 should (s) be for the equations (7x+13y=67) and (21x+39y=s) to be consistent and dependent?Which condition is correct for the equations (11x+6y=37) and (22x+12y=r) to be inconsistent?What will (a) be for the equations (8x+7y=34) and (16x+ay=79) to have no solution?What will (k) be for the equations (10x+ky=110) and (2x+9y=22) to have infinitely many solutions?If (lx+15y=60) and (18x+45y=181) have no solution, what will be the value of (l)?Which statement is correct by observing the equations (16x+11y=73) and (32x+22y=146)?What is the correct conclusion by observing the equations (20x-15y=85) and (4x-3y=18)?What is the correct solution status for the equations (23x+10y=83) and (11x+5y=39)?What is the correct condition on (t) for the equations (4x+7y=31) and (12x+21y=t) to be inconsistent?What is the value of (a) for the equations (5x+ay=45) and (20x+28y=180) to have infinitely many solutions?What is the value of (b) for the equations (bx+9y=36) and (16x+24y=97) to have no solution?Which condition is correct for the equations (13x+py=52) and (6x+5y=24) to have a unique solution?What is the correct solution status for the equations (14x-8y+25=0) and (21x-12y+40=0)?What conclusion follows from comparing the ratios of a and b in 6x + 17y = 71 and 11x + 31y = 130?For prices of two items, the equations (9x+4y=360) and (27x+12y=1090) are formed. What type of system is this?By observing the equations 18x + 5y = 79 and 36x + 10y = 158, which statement is correct?What is the value of (a) for the equations (4x+ay=32) and (12x+21y=96) to have infinitely many solutions?What is the value of (p) for the equations (px+9y=45) and (20x+30y=103) to have no solution?For a pair of linear equations, if \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}\), which statement about their graphical representation is correct?Which conclusion is correct for the equations 7x − 4y = 29 and 21x − 12y = 87?