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
Which ratio relation is correct for the equations (8x+13y-59=0) and (24x+39y-177=0)?What is the correct ratio relation for the equations (12x-5y+37=0) and (24x-10y+79=0)?What is the correct conclusion for the equations (13x+6y-41=0) and (26x+13y-82=0)?If (cx+16y=64) and (21x+42y=130) have no solution, what will (c) be?What is the value of (d) for the equations (6x+dy=54) and (18x+30y=162) to have infinitely many solutions?Which condition is correct for the equations (15x+py=45) and (7x+2y=24) to have a unique solution?If (9x+5y=47) and (27x+15y=n) have infinitely many solutions, what is (n)?For a pair of linear equations in two variables, if \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}\), what is the position of their lines?What is the most suitable conclusion by observing the equations (9x+14y=71) and (27x+42y=213)?Which conclusion is correct by observing the equations (21x+28y=84) and (3x+4y=15)?What is found by comparing the ratios of (a) and (b) in the equations (17x+10y=61) and (8x+5y=29)?What type of pair is formed by the equations (24x+36y=168) and (2x+3y=14)?What type of pair is formed by the equations (22x+33y=99) and (2x+3y=11)?What type of pair is formed by the equations (16x+7y=55) and (8x+4y=29)?In a shop, the equations for two items are (5x+9y=300) and (15x+27y=900). How many solutions will there be?For prices of two tickets, the equations (8x+3y=280) and (16x+6y=575) are formed. What type of system is this?For two numbers, the equations (6x+5y=49) and (3x-2y=7) are formed. What will be the solution status?What is the relation among all three ratios in the equations (9x+16y=74) and (27x+48y=222)?Which relation is correct for the equations (14x+21y=98) and (2x+3y=17)?Which statement is correct for the equations (10x+11y=43) and (20x+21y=84)?