Advertisements
Advertisements
प्रश्न
Solve by the method of elimination
3(2x + y) = 7xy, 3(x + 3y) = 11xy
Advertisements
उत्तर
3(2x + y) = 7xy
6x + 3y = 7xy
Divided by xy
`(6x)/(xy) + (3y)/(xy) = (7xy)/(xy)`
`6/y + 3/x` = 7
Let `1/x` = a, `1/y` = b
3a + 6b = 7 → (1)
3(x + 3y) = 11xy
3x + 9y = 11xy
Divided by xy
`(3x)/(xy) + (9y)/(xy) = (11xy)/(xy)`
`3/y + 9/x` = 11
Let `1/x` = a, `1/y` = b
9a + 3b = 11 → (2)
(1) × 3 ⇒ 9a + 18b = 21 → (3)
(2) × 1 ⇒ 9a + 3b = −11 → (2)
(3) – (2) ⇒ 15b = 10
b = `10/15 = 2/3`
Substitute the value of b = `2/3` in (1)
`3"a" + 6 xx 2/3` = 7
3a + 4 = 7
3a = 7 – 4
3a = 3
a = `3/3`
= 1
But `1/x` = a
`1/x` = 1
x = 1
But `1/y` = b
`1/y = 2/3`
2y = 3
y = `3/2`
∴ The value of x = 1 and y = `3/2`
APPEARS IN
संबंधित प्रश्न
Solve the following pair of linear (simultaneous) equation by the method of elimination by substitution:
1.5x + 0.1y = 6.2
3x - 0.4y = 11.2
Solve th following pair of linear (Simultaneous ) equation using method of elimination by substitution :
`[ 2x + 1]/7 + [5y - 3]/3 = 12`
`[3x + 2 ]/2 - [4y + 3]/9 = 13`
Solve the following simultaneous equations by the substitution method:
2x + y = 8
3y = 3 + 4x
Solve the following simultaneous equations by the substitution method:
2x + 3y = 31
5x - 4 = 3y
The difference of two numbers is 3, and the sum of three times the larger one and twice the smaller one is 19. Find the two numbers.
If a number is thrice the other and their sum is 68, find the numbers.
The ratio of passed and failed students in an examination was 3 : 1. Had 30 less appeared and 10 less failed, the ratio of passes to failures would have been 13 : 4. Find the number of students who appeared for the examination.
Solve by the method of elimination
2x – y = 3, 3x + y = 7
Solve by the method of elimination
13x + 11y = 70, 11x + 13y = 74
Five years ago, a man was seven times as old as his son, while five year hence, the man will be four times as old as his son. Find their present age
