CLASS-10

BOARD: CBSE

Mathematic Worksheet - 3

TOPIC: Linear Equation in two Variables

For other **CBSE Worksheet for class 10 Mathematic** check out main page of Entrancei.

**SUMMARY**

(Standard form of linear equation)

a_{1} +b_{1}y + c_{1 }=0

a_{2}x + b_{2}y+ c_{2}=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 a _{1}x +b_{1}y+c_{1}=0 and a_{2}x +b_{2}y+c_{2} 0, if the denominator a _{1}b_{2}-a _{2}b _{1} 0 then the given system of equation have unique solution and solution are said to be consistent**

**a _{1}b_{2} – a_{2}b_{1} ≠0 i.e.a1/a2≠(b2 )/b1**

**2. No solution**

Two lines a _{1}x+b _{1}y+c _{1}=0 and a _{2}x+b _{2}y+c _{2}=0,if the denominator a _{1}b _{2}-a _{2}b _{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 _{1}x+b _{1}y+c _{1}=0 and a _{2}x+b _{2}y+c_{2}=0 if a1/a2=b1/b2=c1/c2then equation of system has many solutions and solutions are said to be consistent

**OBJECTIVE**

**On solving 25/(x+y)-3/(x-y)=1,40/(x+y)+2/(x-y)=5we get**

A. x=8,y=8

b) x=4,y=6

c) x=6,y=4

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

d) 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

c) Inconsistent

d) Homogenous linear equation

**4) If , then z will be,**

a) y-x

b) x-y

c)y-x/xy

d) xy/y-x

**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) 1/2

b) 2

c) 4

d)1/10

**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**

a) 5km/hr

b) 7.5km/hr

c) 6km/hr

d) 6.25km/hr

**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))

b) (2(x+1))/(y+1)

c) 2(x/y)

d) (2x-1)/(y+1)

**SUBJECTIVE**

**1. Solve i) 7/3 ^{x} -6/2^{y} =15,8/3^{x} =9/2^{y}**

**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)= a^{2}-2ab-b^{2}

ii) (a +b)(x +y)=a^{2}+b^{2}

**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=a^{2}+b^{2} ; 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.**

**Answer:**

**Objective: **

1) c

2) d

3) a

4) d

5) b

6) a

7) a

8) d

**Subjective: **

1) i) x =-2,y=-3

ii) x=-1,y=-2

2)720km

3) 57

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

8) 5/6