Advertisements
Advertisements
प्रश्न
Solve each of the following systems of equations by the method of cross-multiplication
`x/a = y/b`
`ax + by = a^2 + b^2`
Advertisements
उत्तर
`x/a = y/b`
``ax + by = a^2 + b^2`
Here `a_1 = 1/a, b_1 = (-1)/b, c_1 = 0`
`a_2 = a, b_2 = b,c_2 = -(a^2 + b^2)`
By cross multiplication, we get
`x/(-1/b(-(a^2 + b^2))-b(0)) = (-y)/(1/a(-(a^2 + b^2))-a(0)) = 1/(1/a (b) - a xx ((-1)/b))`
`x/((a^2 + b^2)/b) = y/((a^2 + b^2)/a) = 1/(b/a + a/b)`
`x = ((a^2 + b^2)/b)/(b/a + a/b) = ((a^2 +b^2)/b)/((b^2 + a^2)/(ab)) = a`
`y = ((a^2 + b^2)/a)/(b/a + a/b) = ((a^2 + b^2)/b)/((b^2+a^2)/(ab)) = b`
Solution is (a, b)
संबंधित प्रश्न
A thief, after committing a theft, runs at a uniform speed of 50 m/minute. After 2 minutes, a policeman runs to catch him. He goes 60 m in first minute and increases his speed by 5 m/minute every succeeding minute. After how many minutes, the policeman will catch the thief?
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
x – 3y – 3 = 0
3x – 9y – 2 = 0
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 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 :
2x + y = 35
3x + 4y = 65
Solve the following system of equations by the method of cross-multiplication:
`(x + y)/(xy) = 2`
`(x - y)/(xy) = 6`
Solve the following system of equations by the method of cross-multiplication:
`ax + by = (a + b)/2`
3x + 5y = 4
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 following system of equations by the method of cross-multiplication:
`(a - b)x + (a + b)y = 2a^2 - 2b^2`
(a + b)(x + y) = 4ab
Solve the following system of equations by the method of cross-multiplication:
`a^2/x - b^2/y = 0`
`(a^2b)/x + (b^2a)/y = a + b, x, y != 0`
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
Solve the system of equations by using the method of cross multiplication:
3x – 2y + 3 = 0, 4x + 3y – 47 = 0
Solve the system of equations by using the method of cross multiplication:
`5/(x + y) - 2/(x - y) + 1 = 0, 15/(x + y) + 7/(x - y) - 10 = 0`
Solve the system of equations by using the method of cross multiplication:
`a/x - b/y = 0, (ab^2)/x + (a^2b)/y = (a^2 + b^2)`, where x ≠ 0 and y ≠ 0
If `|( 4,5), (m , 3)|` = 22, then find the value of m.
Complete the activity to find the value of x.
3x + 2y = 11 ...(i) and 2x + 3y = 4 ...(ii)
Solution:
Multiply equation (i) by ______ and equation (ii) by ______.
`square` × (3x + 2y = 11) ∴ 9x + 6y = 33 ...(iii)
`square` × (2x + 3y = 4) ∴ 4x + 6y = 8 ...(iv)
Subtract (iv) from (iii),
`square` x = 25
∴ x = `square`
Solve the following pair of equations:
`4x + 6/y = 15, 6x - 8/y = 14, y ≠ 0`
Solve the following pair of equations:
`(2xy)/(x + y) = 3/2, (xy)/(2x - y) = (-3)/10, x + y ≠ 0, 2x - y ≠ 0`
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?
