Advertisements
Advertisements
Question
The sum of four times the first number and three times the second number is 15. The difference of three times the first number and twice the second number is 7. Find the numbers.
Advertisements
Solution
Let the two numbers be x and y respectively.
Then, we have
4x + 3y = 15 ....(i)
3x - 2y = 7 ....(ii)
Multiplying eqn. (i) by 2 and eqn. (ii) by 3, we get
8x + 6y = 30 ....(iii)
9x - 6y = 21 ....(iv)
Adding eqns. (iii) and (iv), we get
17x = 51
⇒ x = 3
⇒ 4(3) + 3y = 15
⇒ 12 + 3y = 15
⇒ 3y = 3
⇒ y = 1
Thus, the two numbers are 3 and 1 respectively.
APPEARS IN
RELATED QUESTIONS
Solve the pair of linear (simultaneous) equation by the method of elimination by substitution :
2x - 3y = 7
5x + y= 9
Solve the following pair of linear (simultaneous) equation by the method of elimination by substitution:
0.2x + 0.1y = 25
2(x - 2) - 1.6y = 116
Solve the pair of linear (simultaneous) equation by the method of elimination by substitution:
6x = 7y + 7
7y - x = 8
Solve the following pair of linear (Simultaneous ) equation using method of elimination by substitution :
2( x - 3 ) + 3( y - 5 ) = 0
5( x - 1 ) + 4( y - 4 ) = 0
Solve the following pair of linear (simultaneous) equation using method of elimination by substitution:
3x + 2y =11
2x - 3y + 10 = 0
Solve the following pair of linear (simultaneous) equation using method of elimination by substitution:
`[3x]/2 - [5y]/3 + 2 = 0`
`x/3 + y/2 = 2 1/6`
Solve the following simultaneous equations by the substitution method:
x + 3y= 5
7x - 8y = 6
Solve the following simultaneous equations by the substitution method:
0.5x + 0.7y = 0.74
0.3x + 0.5y = 0.5
Solve the following simultaneous equations by the substitution method:
3 - (x + 5) = y + 2
2(x + y) = 10 + 2y
Solve the following pairs 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
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.
Samidha and Shreya have pocket money Rs.x and Rs.y respectively at the beginning of a week. They both spend money throughout the week. At the end of the week, Samidha spends Rs.500 and is left with as much money as Shreya had in the beginning of the week. Shreya spends Rs.500 and is left with `(3)/(5)` of what Samidha had in the beginning of the week. Find their pocket money.
Solve by the method of elimination
2x – y = 3, 3x + y = 7
Solve by the method of elimination
3(2x + y) = 7xy, 3(x + 3y) = 11xy
Solve by the method of elimination
13x + 11y = 70, 11x + 13y = 74
