Advertisements
Advertisements
Question
Solve for x and y:
4x = 17 - `[ x - y ]/8`
2y + x = 2 + `[ 5y + 2 ]/3`
Advertisements
Solution
The given pair of linear equations are
4x = 17 - `[ x - y ]/8`
⇒ 33x - y = 136 ...(1) [On Simplifying]
2y + x = 2 + `[ 5y + 2 ]/3`
⇒ 3x + y = 8 ...(2) [On Simplifying]
Multiply equation (2) by 11, we get,
33x + 11y = 88 ...(3)
Subtracting equation (1) from (3)
33x + 11y = 88
- 33x - y = 136
- + -
12y = - 48
y = -4
Substituting y = -4 in equation (1), we get:
33x - (-4) = 136
⇒ 33x = 132
⇒ x = 4
∴ Solution is x = 4 and y = - 4.
APPEARS IN
RELATED QUESTIONS
Solve :
`4x + [ x - y ]/8 = 17`
`2y + x - [ 5y + 2 ]/3 = 2`
Solve the following pairs of equations:
`(3)/(2x) + (2)/(3y)` = 5
`(5)/x - (3)/y` = 1
Solve the following pairs of equations:
`(3)/x - (1)/y` = -9
`(2)/x + (3)/y` = 5
Solve the following pairs of equations:
`(5)/(x + y) - (2)/(x - y)` = -1
`(15)/(x + y) + (7)/(x - y)` = 10.
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.
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.
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.
The sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes `(1)/(2)`. Find the fraction.
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?
