Advertisements
Advertisements
Question
Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions. In case there is a unique solution, find it by using cross multiplication method
3x – 5y = 20
6x – 10y = 40
Solution
3x – 5y = 20
6x – 10y = 40
`a_1/a_2 = 3/6 = 1/2`
`b_1/b_2 = (-5)/-10 = 1/2`
`c_1/c_2 = (-20)/-40 = 1/2`
`a_1/a_2 = b_1/b_2 = c_1/c_2`
Therefore, the given sets of lines will be overlapping each other i.e., the lines will be coincident to each other and thus, there are infinite solutions possible for these equations.
APPEARS IN
RELATED QUESTIONS
Solve the following system of equations in x and y by cross-multiplication method
`(a – b) x + (a + b) y = a^2 – 2ab – b^2`
`(a + b) (x + y) = a^2 + b^2`
Which of the following pairs of linear equations has unique solution, no solution or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method
2x + y = 5
3x + 2y = 8
Solve the following systems of equations:
`sqrt2x + sqrt3y = 0`
`sqrt3x - sqrt8y = 0`
Solve the following systems of equations:
`1/(7x) + 1/(6y) = 3`
`1/(2x) - 1/(3y) = 5`
Solve each of the following systems of equations by the method of cross-multiplication :
`x(a - b + (ab)/(a - b)) = y(a + b - (ab)/(a + b))`
`x + y = 2a^2`
Solve the system of equations by using the method of cross multiplication:
7x - 2y – 3 = 0,
`11x - 3/2 y – 8 = 0.`
Solve the system of equations by using the method of cross multiplication:
`x/6 + y/15 – 4 = 0, x/3 - y/12 – 19/4 = 0`
Solve the following pair of equations:
`1/(2x) - 1/y = -1, 1/x + 1/(2y) = 8, x, y ≠ 0`
Solve the following pair of equations:
43x + 67y = – 24, 67x + 43y = 24
A railway half ticket costs half the full fare, but the reservation charges are the same on a half ticket as on a full ticket. One reserved first class ticket from the station A to B costs Rs 2530. Also, one reserved first class ticket and one reserved first class half ticket from A to B costs Rs 3810. Find the full first class fare from station A to B, and also the reservation charges for a ticket.
