Advertisements
Advertisements
प्रश्न
If 10y = 7x - 4 and 12x + 18y = 1; find the values of 4x + 6y and 8y - x.
Advertisements
उत्तर
10 y = 7x - 4
- 7x + 10y = - 4
- (7x - 10y) = 4
7x - 10y = 4 ...(1)
12x + 18y = 1 ...(2)
Multiplying equation no. (1) by 12 and (2) by 7.
84x - 120y = 48 ....(3)
84x + 126y = 7 ....(4)
Substract equation (3) and (4)
84x - 120y = 48
84x + 126y = 7
(-) (-) (-)
- 246 y = 41
y = `41/(- 246)`
y = - `1/6`
From (1)
7x - 10`(-1/6)` = 4
7x + `5/3` = 4
7x = `4 - 5/3`
7x = `7/3`
x = `7/3 xx 7`
x = `1/3`
∴ 4x + 6y = `4(1/3) + 6(-1/6) = 4/3 - 6/6 = 4/3 - 1 = 1/3`
∴ 8y - x = `8(-1/6) - 1/3 = -4/3 - 1/3 = -5/3`
APPEARS IN
संबंधित प्रश्न
For solving pair of equation, in this exercise use the method of elimination by equating coefficients :
13 + 2y = 9x
3y = 7x
For solving pair of equation, in this exercise use the method of elimination by equating coefficients :
3 - (x - 5) = y + 2
2 (x + y) = 4 - 3y
If 2x + y = 23 and 4x - y = 19; find the values of x - 3y and 5y - 2x.
Solve the following simultaneous equations:
103a + 51b = 617
97a + 49b = 583
Can the following equations hold simultaneously?
7y - 3x = 7
5y - 11x = 87
5x + 4y = 43
If yes, find the value of x and y.
The length of a rectangle is twice its width. If its perimeter is 30 units, find its dimensions.
In a two-digit number, the sum of the digits is 7. The difference of the number obtained by reversing the digits and the number itself is 9. Find the number.
The ratio of two numbers is `(2)/(5)`. If 4 is added in first and 32 is subtracted from the second, the ratio becomes the reciprocal of the original ratio. Find the numbers.
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 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?
