Advertisements
Advertisements
प्रश्न
By equating coefficients of variables, solve the following equation.
x − 2y = −10 ; 3x − 5y = −12
Advertisements
उत्तर
x − 2y = −10 ...(I)
3x − 5y = −12 ...(II)
Multiply (I) with 3
3x − 6y = −30 ...(III)
Subtracting (II) from (III) we get,
3x − 6y = −30
3x − 5y = −12
- + +
−y = −18
⇒ y = 18
Putting the value of y in (I) we get,
∴ x − 2y = −10
⇒ x − 2 × 18 = −10
⇒ x = −10 + 36 = 26
Thus, x = 26, y = 18
APPEARS IN
संबंधित प्रश्न
Solve the following system of equations: 15x + 4y = 61; 4x + 15y = 72
Solve the following system of linear equations by using the method of elimination by equating the coefficients √3x – √2y = √3 = ; √5x – √3y = √2
Solve for x and y : `\frac { ax }{ b } – \frac { by }{ a } = a + b ; ax – by = 2ab`
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:
The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.
Form the pair of linear equation in the following problem, and find its solution (if they exist) by the elimination method:
A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid Rs 27 for a book kept for seven days, while Susy paid Rs 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.
The sum of a two-digit number and the number formed by reversing the order of digit is 66. If the two digits differ by 2, find the number. How many such numbers are there?
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`
Solve the following simultaneous equation.
`x/3 + 5y = 13 ; 2x + y/2 = 19`
Solve the following simultaneous equation.
`2/x + 3/y = 13` ; `5/x - 4/y = -2`
By equating coefficients of variables, solve the following equation.
4x + y = 34 ; x + 4y = 16
If 52x + 65y = 183 and 65x + 52y = 168, then find x + y = ?
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 solution of the equation ax + by + 5 = 0 and bx – ay – 12 = 0 is (2, – 3). Find the values of a and b.
The angles of a triangle are x, y and 40°. The difference between the two angles x and y is 30°. Find x and y.
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.
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.
Read the following passage:
Two schools 'P' and 'Q' decided to award prizes to their students for two games of Hockey ₹ x per student and Cricket ₹ y per student. School 'P' decided to award a total of ₹ 9,500 for the two games to 5 and 4 Students respectively; while school 'Q' decided to award ₹ 7,370 for the two games to 4 and 3 students respectively. |
Based on the above information, answer the following questions:
- Represent the following information algebraically (in terms of x and y).
- (a) What is the prize amount for hockey?
OR
(b) Prize amount on which game is more and by how much? - What will be the total prize amount if there are 2 students each from two games?
