Advertisements
Advertisements
Question
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.
Advertisements
Solution
Let the larger number be x and the smaller number be y.
According to given information, we have
x - y = 3
⇒ x - 3 + y ....(i)
Also, 3x + 2y = 19
⇒ 3(3 + y) + 2y = 19 ....[From (i)]
⇒ 9 + 3y + 2y = 19
⇒ 5y = 10
⇒ y = 2
⇒ x = 3 + 2
= 5
Thus, the required numbers are 5 and 2 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 pair of linear (simultaneous) equation by the method of elimination by substitution:
2x + 7y = 39
3x + 5y = 31
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 :
2x - 3y + 6 = 0
2x + 3y - 18 = 0
Solve the following simultaneous equations by the substitution method:
2x + y = 8
3y = 3 + 4x
Solve the following simultaneous equations by the substitution method:
5x + 4y - 23 = 0
x + 9 = 6y
Solve the following simultaneous equations by the substitution method:
2x + 3y = 31
5x - 4 = 3y
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:
0.4x + 0.3y = 1.7
0.7x - 0.2y = 0.8
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 age of the father is seven times the age of the son. Ten years later, the age of the father will be thrice the age of the son. Find their present ages.
In a ABC, ∠A = x°, ∠B = (2x - 30)°, ∠C = y° and also, ∠A + ∠B = one right angle. Find the angles. Also, state the type of this triangle.
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
The monthly income of A and B are in the ratio 3 : 4 and their monthly expenditures are in the ratio 5 : 7. If each saves ₹ 5,000 per month, find the monthly income of each
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
