Advertisements
Advertisements
प्रश्न
Solve each of the following systems of equations by the method of cross-multiplication :
`b/a x + a/b y - (a^2 + b^2) = 0`
x + y - 2ab = 0
Advertisements
उत्तर
The given system of the equation may be written as
`b/a x + a/b y - (a^2 + b^2) = 0``
x + y - 2ab = 0
Here
`a_1 = b/a, b_1 =- a/b,c_1 = -(a^2 + b^2)`
`a_2 = 1, b_2 = 1, c_2 = -2ab`
By cross multiplication, we have
`x/(-2ab xx a/b + a^2 + b^2) = (-y)/(-2ab xx a/b + a^2 + b^2) = 1/(b/a - a/b)`
`=> x/(-2a^2 + a^2 + b^2) = (-y)/(-2b^2 + a^2 + b^2) = 1/((b^2 - a^2)/(ab))`
`=> x/(b^2 - a^2) = (-y)/(-b^2 + a^2) = 1/((b^2 - a^2)/(ab))`
Now
`x/(b^2 - a^2) = 1/((b^2 - a^2)/(ab))`
`=> x = b^2 - a^2 aa (ab)/(b^2 - a^2)`
=> x = ab
And
`(-y)/(-b^2 + a^2) = 1/((b^2 - a^2)/(ab))`
`=> -y = b^2 + a^2 xx (ab)/(b^2 - a^2)`
`=> -y =-(b^2 - a^2) xx (ab)/(b^2 - a^2)``
=> -y = -ab
=> y = ab
Hence, x = ab,y = ab is the solution of the given system of equations.
संबंधित प्रश्न
Solve the follownig system of equations by the method of cross-multiplication.
2x – 6y + 10 = 0
3x – 7y + 13 = 0
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
x – 3y – 3 = 0
3x – 9y – 2 = 0
For which value of k will the following pair of linear equations have no solution?
3x + y = 1
(2k – 1)x + (k – 1)y = 2k + 1
Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method:
A fraction becomes `1/3` when 1 is subtracted from the numerator and it becomes `1/4` when 8 is added to its denominator. Find the fraction.
Solve the following systems of equations:
`x + 2y = 3/2`
`2x + y = 3/2`
Solve the following systems of equations:
`2x - 3/y = 9`
`3x + 7/y = 2, y != 0`
Solve the following system of equations:
0.5x + 0.7y = 0.74
0.3x + 0.5y = 0.5
Solve the following system of equations:
`4/x + 3y = 14`
`3/x - 4y = 23`
Solve each of the following systems of equations by the method of cross-multiplication :
x + 2y + 1 = 0
2x − 3y − 12 = 0
Solve each of the following systems of equations by the method of cross-multiplication
x + ay = b
ax − by = c
Solve each of the following systems of equations by the method of cross-multiplication
`x/a + y/b = 2`
`ax - by = a^2 - b^2`
Solve each of the following systems of equations by the method of cross-multiplication :
`5/(x + y) - 2/(x - y) = -1`
`15/(x + y) + 7/(x - y) = 10`
where `x != 0 and y != 0`
Solve the system of equations by using the method of cross multiplication:
x + 2y + 1 = 0, 2x – 3y – 12 = 0
Solve the system of equations by using the method of cross multiplication:
3x + 2y + 25 = 0, 2x + y + 10 = 0
Solve the system of equations by using the method of cross multiplication:
2x + y – 35 = 0, 3x + 4y – 65 = 0
Solve the system of equations by using the method of cross multiplication:
`1/x + 1/y = 7, 2/x + 3/y = 17`
If `|( 4,5), (m , 3)|` = 22, then find the value of m.
Solve the following pair of equations:
43x + 67y = – 24, 67x + 43y = 24
Susan invested certain amount of money in two schemes A and B, which offer interest at the rate of 8% per annum and 9% per annum, respectively. She received Rs 1860 as annual interest. However, had she interchanged the amount of investments in the two schemes, she would have received Rs 20 more as annual interest. How much money did she invest in each scheme?
