Advertisements
Advertisements
Question
Show that the system of equations
6x + 5y = 11,
9x + 152 y = 21
has no solution.
Solution
The given system of equations can be written as
6x + 5y – 11 = 0 ….(i)
`⇒9x + 15/2 y - 21 = 0` …(ii)
This system is of the form
`a_1x+b_1y+c_1 = 0`
`a_2x+b_2y+c_2 = 0`
Here, `a_1 = 6, b_1= 5, c_1= -11 and a_2 = 9, b_2= 15/2 , c_2= -21`
Now,
`(a_1)/(a_2) = 6/9 = 2/3`
`(b_1)/(b_2) = 5/(15/2) = 2/3`
`(c_1)/(c_2) = (−11)/(−21) = 11/21`
Thus, `(a_1)/(a_2) = (b_1)/(b_2 )≠ (c_1)/(c_2)`, therefore the given system has no solution.
APPEARS IN
RELATED QUESTIONS
Draw a graph of the line x – 2y = 3. From the graph, find the coordinates of the point when (i) x = – 5 (ii) y = 0.
Find the value of k for which each of the following system of equations has infinitely many solutions
kx - 2y + 6 = 0
4x + 3y + 9 = 0
Solve for x and y:
4x - 3y = 8, 6x - y = `29/3`
For what value of k, the system of equations
x + 2y = 3,
5x + ky + 7 = 0
Have (i) a unique solution, (ii) no solution?
Also, show that there is no value of k for which the given system of equation has infinitely namely solutions
Find the value of k for which the system of linear equations has an infinite number of solutions:
2x + (k – 2)y = k,
6x + (2k - 1)y = (2k + 5).
Find the value of k for which the system of equations
kx + 3y = 3, 12x + ky = 6 has no solution.
A lady has only 50-paisa coins and 25-paisa coins in her purse. If she has 50 coins in all totaling Rs.19.50, how many coins of each kind does she have?
The denominator of a fraction is greater than its numerator by 11. If 8 is added to both its numerator and denominator, it becomes `3/4`. Find the fraction.
A sailor goes 8 km downstream in 420 minutes and returns in 1 hour. Find the speed of the sailor in still water and the speed of the current .
One equation of a pair of dependent linear equations is –5x + 7y = 2. The second equation can be ______.
