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If you are looking NCERT Solutions for Class 10 Maths error free and prepared by experienced mentors. Don’t WORRY!! Here we are providing Free PDF you can get easy with a single click SUMMARY (Standard form of linear equation) a1 +b1y + c1 =0 a2x + b2y+ c2=0 For solving such equation we have three methods. a) Elimination by substitution b) Elimination by equating the coefficients c) Elimination by cross multiplication CONDITION FOR SOLVALIBILITY (OR CONSISTENCY) OF SYSTEM OF EQUATION a) Unique Solution Two lines a1x +b1y+c1=0 and a2x +b2y+c2≠0, if the denominator a 1b2-a 2b 1≠0 then the given system of equation have unique solution and solution are said to be consistent a1b2– a2b1≠0 i.e. a1 a2≠ b) No solution Two lines a 1x+b 1y+c 1=0 and a 2x+b 2y+c 2=0,if the denominator a 1b 2-a 2b 1=0 then the given system of equation have no solution and solution are said to be consistent and the solution are said to be inconsistent i.e. a1 c) Many Solutions Two lines a 1x+b 1y+c 1=0 and a 2x+b 2y+c2=0 if ?1 solutions and solutions are said to be consistent OBJECTIVE 1) On solving ?+?− a)x=8,y=8 b) x=4,y=6 c) x=6,y=4 2 ) If the system 2x +3y-5=0 ,4x +ky -10=0has an infinite number of solution then a) k =3 3) The equation x+2y=4 and 2x+y=5 are a) Consistent and have a unique solution. b) Consistent and have infinitely many solution c) Inconsistent d) Homogenous linear equation 4) If 1 ?− a) y-x b) x-y c) ?−? 5) The graph of 2x+3y-6=0, 4x-3y-6=0 intersect at a) Four points b) one point c)two points d) infinite no. of points 6) The sum of two numbers is 20.their product is 40.The sum of their reciprocal is : a) 1 c) 4 b2 b1 a2 ≠ b1 b2 ≠ c1 c2 ?1 ?2= ?1 ?2 then equation of system has many ?2= 25 3 40 ?+?+ 2 ?−?= 5 we get ?−?= 1, d) None of these 3 2 c) k≠ 6 2 b) k≠ d) k=6 1 ?= 1 ? , then z will be, ?? ?−?. ?? d) d) 1 2 b) 2 10 HURRY!! Visit our portal and get your NCERT Solutions UPDATED 2021-22. These all very essential for your exam preparation
If you are looking NCERT Solutions for Class 10 Maths error free and prepared by experienced mentors. Don’t WORRY!! Here we are providing Free PDF you can get easy with a single click 7) 8) SUBJECTIVE 1) Solve i)7 2) A train covered a certain distance at a uniform speed. If the train would have been 6km/hr faster, It would have taken 4 hrs less than the scheduled time. And if the train were slower by 6km/hr. it would have taken 6 hrs more than the scheduled time. Find the length of the journey. 3) The sum of the two digit numbers is 12.The number obtained by interchanging the two digits exceeds the given number by 18.Find the number. 4) Abdul travelled 300km by train and 200 km by taxi taking 5 hrs 30 minutes but if he travels 260km by train and 240 by taxi he takes 6 minutes longer. Find the speed of the train and that of taxi. 5) Solve for x and y i) (a-b)x+(a+b)= a2-2ab-b2 ii) (a +b)(x +y)=a2+b2 6) Solve for x and y ?? 7) Solve the following pair of linear equation for x and y ? 8) The sum of the numerator and the denominator of fraction is 4 more than twice the numerator. If 3 is added to each of the numerator and denominator their ratio becomes 2:3. Find the fraction. Answer: In covering a distance of 30 km Amit takes 2 hrs more than suresh. If Amit doubles his speed, he would take one hr. less than Suresh Amit’s speed is a) 5km/hr b) 7.5km/hr c) 6km/hr d) 6.25km/hr If in a fraction 1 is subtracted from two times of numerator x and 1 is added in denominator y then new fraction will be: a) 2(?−1 ?+1) b) 2(?+1) ?+1 c) 2(? ?) d) 2?−1 ?+1 6 8 3?= 9 2? 3?− ii) 119x -381y=643; 381x-119y=-143. 2?= 15, ?−?? ?= ? + ?; ax-by=2ab ?? +? ?? = ?2+ ?2; x+y=2ab HURRY!! Visit our portal and get your NCERT Solutions UPDATED 2021-22. These all very essential for your exam preparation
If you are looking NCERT Solutions for Class 10 Maths error free and prepared by experienced mentors. Don’t WORRY!! Here we are providing Free PDF you can get easy with a single click Objective: Subjective: 1) c 5) b 2) d 3) a 4) d 6) a 7) a 8) d 1) i) x =-2,y=-3 ii) x=-1,y=-2 2)720km 3) 57 5) x=a + b; y=−2?? 4) Speed of train =100km/hr; Speed of taxi = 80km/hr ?+? 8) 5 6) x=b; y= -a 7) x =a b; y=a b 9 HURRY!! Visit our portal and get your NCERT Solutions UPDATED 2021-22. These all very essential for your exam preparation