Advertisements
Advertisements
Question
Solve :
11(x - 5) + 10(y - 2) + 54 = 0
7(2x - 1) + 9(3y - 1) = 25
Advertisements
Solution
11( x - 5 ) + 10( y - 2 ) + 54 = 0 (given)
⇒ 11x - 55 + 10y - 20 + 54 = 0
⇒ 11x + 10y - 21 = 0
⇒ 11x + 10y = 21 ....(1)
7( 2x - 1 ) + 9(3y - 1) = 25 (given)
⇒ 14x - 7 + 27y - 9 = 25
⇒ 14x + 27y - 16 = 25
⇒ 14x + 27y = 41 .....(2)
Multiplying equation (1) by 27 and equation (2) by 10, we get,
297x + 270y = 567 ....(3)
140x + 270y = 410 .....(4)
Subtracting equation (4) from equation (3), we get
157x = 157
⇒ x = 1
Substituting x = 1 in equation (1), we get,
11 x 1 + 10y = 21
⇒ 10y = 10
⇒ y = 1
∴ Solution set is x = 1 and y = 1.
APPEARS IN
RELATED QUESTIONS
For solving pair of equation, in this exercise use the method of elimination by equating coefficients :
41x + 53y = 135
53x + 41y = 147
Solve for x and y :
`[ y + 7 ]/5 = [ 2y - x ]/4 + 3x - 5`
`[ 7 - 5x ]/2 + [ 3 - 4y ]/6 = 5y - 18`
Solve the following simultaneous equation :
8v - 3u = 5uv
6v - 5u = -2uv
`(3)/x - (2)/y` = 0 and `(2)/x + (5)/y` = 19, Hence, find a if y = ax + 3.
The sum of a two-digit number and the number obtained by reversing the digits is 110 and the difference of two digits is 2. Find the number.
If 1 is added to the denominator of a fraction, the fraction becomes `(1)/(2)`. If 1 is added to the numerator of the fraction, the fraction becomes 1. Find the fraction.
Anil and Sunita have incomes in the ratio 3 : 5. If they spend in the ratio 1 : 3, each saves T 5000. Find the income of each.
An eraser costs Rs. 1.50 less than a sharpener. Also, the cost of 4 erasers and 3 sharpeners is Rs.29. Taking x and y as the costs (in Rs.) of an eraser and a sharpener respectively, write two equations for the above statements and find the value of x and y.
A person goes 8 km downstream in 40 minutes and returns in 1 hour. Determine the speed of the person in still water and the speed of the stream.
A solution containing 12% alcohol is to be mixed with a solution containing 4% alcohol to make 20 gallons of solution containing 9% alcohol. How much of each solution should be used?
