Advertisements
Advertisements
प्रश्न
By equating coefficients of variables, solve the following equations.
3x - 4y = 7; 5x + 2y = 3
Advertisements
उत्तर
3x - 4y = 7 ...(I)
5x + 2y = 3 ...(II)
Multiply (II) with 2
10x + 4y = 6 ...(III)
Adding (I) and (III)
3x - 4y = 7
10x + 4y = 6
13x = 13
⇒ x = 1
Putting the value of x in (I) we get
∴ 3x - 4y = 7
⇒ 3 × 1 - 4y = 7
⇒ 3 - 4y = 7
⇒ y = -1
Thus, x = 1 and y = -1
APPEARS IN
संबंधित प्रश्न
Solve the following system of linear equations by using the method of elimination by equating the coefficients: 3x + 4y = 25 ; 5x – 6y = – 9
Solve (a – b) x + (a + b) y = `a^2 – 2ab – b^2 (a + b) (x + y) = a^2 + b^2`
Solve the following pair of linear equation by the elimination method and the substitution method:
x + y = 5 and 2x – 3y = 4
Solve the following pair of linear equation by the elimination method and the substitution method:
3x + 4y = 10 and 2x – 2y = 2
Solve the following pair of linear equation by the elimination method and the substitution method.
3x – 5y – 4 = 0 and 9x = 2y + 7
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`
In an envelope there are some 5 rupee notes and some 10 rupee notes. Total amount of these notes together is 350 rupees. Number of 5 rupee notes are less by 10 than twice number of 10 rupee notes. Then find the number of 5 rupee and 10 rupee notes.
Sanjay gets fixed monthly income. Every year there is a certain increment in his salary. After 4 years, his monthly salary was Rs. 4500 and after 10 years his monthly salary became 5400 rupees, then find his original salary and yearly increment.
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.
Ajay is younger than Vijay by 5 years. Sum of their ages is 25 years. What is Ajay's age?
Solve the following simultaneous equation.
x − 2y = −2 ; x + 2y = 10
Solve the following simultaneous equation.
`x/3 + 5y = 13 ; 2x + y/2 = 19`
By equating coefficients of variables, solve the following equation.
x − 2y = −10 ; 3x − 5y = −12
The difference between an angle and its complement is 10° find measure of the larger angle.
If 52x + 65y = 183 and 65x + 52y = 168, then find x + y = ?
Complete the activity.
The sum of the two-digit number and the number obtained by interchanging the digits is 132. The digit in the ten’s place is 2 more than the digit in the unit’s place. Complete the activity to find the original number.
Activity: Let the digit in the unit’s place be y and the digit in the ten’s place be x.
∴ The number = 10x + y
∴ The number obtained by interchanging the digits = `square`
∴ The sum of the number and the number obtained by interchanging the digits = 132
∴ 10x + y + 10y + x = `square`
∴ x + y = `square` .....(i)
By second condition,
Digit in the ten’s place = digit in the unit’s place + 2
∴ x – y = 2 ......(ii)
Solving equations (i) and (ii)
∴ x = `square`, y = `square`
Ans: The original number = `square`
The sum of the digits of a two-digit number is 9. If 27 is added to it, the digits of the number get reversed. The number is ______.
