Advertisements
Advertisements
Question
Solve the following simultaneous equations:
103a + 51b = 617
97a + 49b = 583
Solution
The given equations are
103a + 51b = 617 ....(i)
97a + 49b = 583 ....(ii)
Subtracting eqn. (ii) from (i). we get
6a + 2b = 34
⇒ 3a + b = 17 ....[Dividing throughtout by 2] ....(iii)
200a + 100b = 1200
⇒ 2a + b = 12 ...[Dividing throughtout by 100] ....(iv)
Subtracting eqn. (iv) from eqn. (iii), we get
a = 5
Substituting the value of an in eqn. (iii), we get
3(5) + b = 17
⇒ 15 + b = 17
⇒ b = 2
Thus, the solution set is (5,2).
APPEARS IN
RELATED QUESTIONS
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 :
3x - y = 23
`x/3 + y/4 = 4`
For solving pair of equation, in this exercise use the method of elimination by equating coefficients :
2x - 3y - 3 = 0
`[2x]/3 + 4y + 1/2` = 0
Solve for x and y:
4x = 17 - `[ x - y ]/8`
2y + x = 2 + `[ 5y + 2 ]/3`
10% of x + 20% of y = 24
3x - y = 20
Solve the following pairs of equations:
`(5)/(x + y) - (2)/(x - y)` = -1
`(15)/(x + y) + (7)/(x - y)` = 10.
`4x + 6/y = 15 and 6x - 8/y = 14.` Hence, find a if y = ax - 2.
Can the following equations hold simultaneously?
7y - 3x = 7
5y - 11x = 87
5x + 4y = 43
If yes, find the value of x and y.
If 2 is added to the numerator and denominator it becomes `(9)/(10)` and if 3 is subtracted from the numerator and denominator it becomes `(4)/(5) `Find the fraction.
A and B can build a wall in `6(2)/(3)` days. If A's one day work is `1(1)/(4)` of one day work of B, find in 4 how many days A and B alone can build the wall.
