Advertisements
Advertisements
Question
Solve the following systems of equations:
`x/7 + y/3 = 5`
`x/2 - y/9 = 6`
Solution
The given system of equation is
`x/7 + y/3 = 5` ...(i)
`x/2 - y/9 = 6`.....(ii)
From (i), we get
`=> (3x + 7y)/21 = 5`
`=> 3x + 7x = 105`
`=> 3x = 1.5 - 7y`
`=> x = (105 - 7y)/3`
From (ii), we get
`(9x - 2y)/18 = 6`
=> 9x - 2y = 108......(iii)'
Substituting x = `(105 - 7y)/3` in (iii) we get
`9(105 - 7y)/3 - 2u = 108`
`=> (948 - 63y)/3 - 2y = 108`
=> 945 - 63y - 6y = 108 x 3
=> 945 - 69y = 324
`=> 945 - 324 = 69y`
=> 69y = 621
=> y = 621/69 = 9
Putting y = 9in x = `(1105 - 7y)/3` we get
`x = (105 - 7 xx 9)/3 = (105 - 63)/3`
`= x = 42/3 = 14`
Hence, the solution of thee given system of equations is x = 14, y = 9
APPEARS IN
RELATED QUESTIONS
Solve the following systems of equations:
7(y + 3) − 2(x + 2) = 14
4(y − 2) + 3(x − 3) = 2
Solve the following systems of equations:
`6/(x + y) = 7/(x - y) + 3`
`1/(2(x + y)) = 1/(3(x - y))`, where x + y ≠ 0 and x – y ≠ 0
Solve the following systems of equations:
23x − 29y = 98
29x − 23y = 110
5 books and 7 pens together cost Rs 79 whereas 7 books and 5 pens together cost Rs 77. Find the total cost of 1 book and 2 pens.
Solve the following set of simultaneous equation.
2x + y = 5; 3x - y = 5
Solve the following set of simultaneous equation.
2x + 3y + 4 = 0; x − 5y = 11
Solve the following set of simultaneous equation.
2x - 7y = 7; 3x + y = 22
Using variables a and b write any two equations whose solution is (0, 2).
The difference between a two digit number and the number obtained by interchanging the digits is 27. What is the difference betw een the two digits of the number?
Solve x + 2y = 10 and 2x + y = 14 by substitution method and hence find the value of m for which y = mx + 8.
