(Standard form of linear equation)
a_{1} +b_{1}y + c_{1 }=0
a_{2}x + b_{2}y+ c_{2}=0
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
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
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
Q1. On solving 25/(x+y)-3/(x-y)=1,40/(x+y)+2/(x-y)=5we get
Q2. If the system 2x +3y-5=0 ,4x +ky -10=0has an infinite number of solution then
Q3. The equation x+2y=4 and 2x+y=5 are
Q4. If , then z will be,
Q5. The graph of 2x+3y-6=0, 4x-3y-6=0 intersect at
Q6. The sum of two numbers is 20.their product is 40.The sum of their reciprocal is:
Q7. 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
Q8. 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:
SUBJECTIVe
Q1. Solve i) 7/3^{x} -6/2^{y} =15,8/3^{x} =9/2^{y}
ii) 119x -381y=643; 381x-119y=-143.
Q2. 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.
Q3. 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.
Q4. 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.
Q5. Solve for x and y
Q6. Solve for x and y ax/b-by/a=a+b ; ax-by=2ab
Q7. Solve the following pair of linear equation for x and y
b/a x+a/b y=a^{2}+b^{2} ; x+y=2ab
Q8. 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:
Subjective:
Q1. i) x =-2,y=-3
ii) x=-1,y=-2
Q2. 720km
Q3. 57
Q4. Speed of train =100km/hr; Speed of taxi = 80km/hr
Q5. x=a + b; y= -2ab/a+b
Q6. x=b; y= -a
Q7. x =a b; y=a b
Q8. 5/6