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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 will be shown in the graph of (12x+8y=44) and (3x+2y=11)?What is the correct description of the graph of (3x+8y=20) and (7x+13y=34)?If two lines have the same slope and the same intercept, what will be the type of the pair?If two lines have the same slope but different intercepts, what is the correct conclusion?Which ratio relation is correct for (3x+5y-20=0) and (9x+15y-60=0)?What is the correct ratio relation for (6x-7y+9=0) and (12x-14y+25=0)?What is the correct conclusion for (7x+4y-13=0) and (14x+9y-26=0)?If (ax+6y=18) and (10x+15y=47) have no solution, what will (a) be?If the two linear equations \(a_1x+b_1y+c_1=0\) and \(a_2x+b_2y+c_2=0\) satisfy \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\), what will be the nature of their lines and the number of solutions?Which condition is correct for (9x+py=27) and (3x+5y=11) to have a unique solution?If (6x+5y=31) and (12x+10y=n) have infinitely many solutions, what is (n)?If 8x − 4y = 24 and 2x − y = t are inconsistent, what is the correct condition for t?What is the most suitable conclusion by observing (5x+3y=17) and (15x+9y=51)?Which conclusion is correct by observing (6x+12y=18) and (x+2y=4)?What is found by comparing the ratios of (a) and (b) in (9x+4y=21) and (4x+2y=10)?What type of pair is 14x+21y=70 and 2x+3y=10?What type of pair is (12x+18y=42) and (2x+3y=8)?If, for the pair of linear equations \(a_1x+b_1y+c_1=0\) and \(a_2x+b_2y+c_2=0\), \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}\), what will be the solution status of the pair?In a shop, the equations for two items are (2x+3y=90) and (4x+6y=180). How many solutions will there be?For prices of two tickets, the equations (4x+3y=120) and (8x+6y=250) are formed. What type of system is this?