Advertisements
Advertisements
Question
By equating coefficients of variables, solve the following equation.
4x + y = 34 ; x + 4y = 16
Solution
4x + y = 34 ...(I)
x + 4y = 16 ...(II)
Adding (I) and (II) we get,
4x + y = 34
x + 4y = 16
5x + 5y = 50
⇒ x + y = 10 ...(III)
Subtracting (II) from (I) we get,
4x + y = 34
x + 4y = 16
- - -
3x - 3y = 18
⇒ x - y = 6 ...(IV)
Adding (III) and (IV) we get,
x + y = 10
x - y = 6
2x = 16
⇒ x = 8
Putting the value of x in (I) we get,
∴ 4x + y = 34
⇒ 4 (8) + y = 34
⇒ y = 34 - 32
⇒ y = 2
Thus, x = 8, y = 2
APPEARS IN
RELATED QUESTIONS
Solve the following pair of linear equation by the elimination method and the substitution method.
`x/2 + (2y)/3 = -1 and x - y /3 = 3`
Form the pair of linear equation in the following problem, and find its solution (if they exist) by the elimination method:
If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes `1/2` if we only add 1 to the denominator. What is the fraction?
The sum of the digits in a two-digits number is 9. The number obtained by interchanging the digits exceeds the original number by 27. Find the two-digit number.
Solve the following simultaneous equation.
`x/3 + y/4 = 4; x/2 - y/4 = 1`
A fraction becomes `1/3` when 2 is subtracted from the numerator and it becomes `1/2` when 1 is subtracted from the denominator. Find the fraction.
A fraction becomes `(1)/(3)` when 2 is subtracted from the numerator and it becomes `(1)/(2)` when 1 is subtracted from the denominator. Find the fraction.
The age of the father is twice the sum of the ages of his two children. After 20 years, his age will be equal to the sum of the ages of his children. Find the age of the father.
Evaluate: (1004)3
A 2-digit number is such that the product of its digits is 24. If 18 is subtracted from the number, the digits interchange their places. Find the number.
Rehana went to a bank to withdraw ₹ 2000. She asked the cashier to give her ₹ 50 and ₹ 100 notes only. Rehana got 25 notes in all. Find how many notes of ₹ 50 and ₹ 100 did she received.
