Mathematic Worksheet - 3
TOPIC: Linear Equation in two Variables
For other CBSE Worksheet for class 10 Mathematic check out main page of Entrancei.
(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
1. 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≠(b2 )/b1
2. 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/a2 ≠ b1/b2 ≠ c1/c2
c) Many Solutions
Two lines a 1x+b 1y+c 1=0 and a 2x+b 2y+c2=0 if a1/a2=b1/b2=c1/c2then equation of system has many solutions and solutions are said to be consistent
On solving 25/(x+y)-3/(x-y)=1,40/(x+y)+2/(x-y)=5we get
d) None of these
2 ) If the system 2x +3y-5=0 ,4x +ky -10=0has an infinite number of solution then
a) k = 3/2
b) k ≠3/2
c) k ≠6
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
d) Homogenous linear equation
4) If , then z will be,
5) The graph of 2x+3y-6=0, 4x-3y-6=0 intersect at
a) Four points
b) one point
d) infinite no. of points
6) The sum of two numbers is 20.their product is 40.The sum of their reciprocal is :
7) 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
8) 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 ((x-1)/(y+1))
1. Solve i) 7/3x -6/2y =15,8/3x =9/2y
ii) 119x -381y=643; 381x-119y=-143.
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 ax/b-by/a=a+b ; ax-by=2ab
7) Solve the following pair of linear equation for x and y
b/a x+a/b y=a2+b2 ; x+y=2ab
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.
1) i) x =-2,y=-3
4) Speed of train =100km/hr; Speed of taxi = 80km/hr
5) x=a + b; y= -2ab/a+b
6) x=b; y= -a
7) x =a b; y=a b