Advertisements
Advertisements
प्रश्न
By equating coefficients of variables, solve the following equation.
x − 2y = −10 ; 3x − 5y = −12
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 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.
`x/2 + (2y)/3 = -1 and x - y /3 = 3`
If the length of a rectangle is reduced by 5 units and its breadth is increased by 3 units, then the area of the rectangle is reduced by 9 square units. If length is reduced by 3 units and breadth is increased by 2 units, then the area of rectangle will increase by 67 square units. Then find the length and breadth of the rectangle.
Solve the following simultaneous equation.
x + y = 11 ; 2x - 3y = 7
Complete the following table to draw the graph of 3x − 2y = 18
| x | 0 | 4 | 2 | −1 |
| y | − 9 | ______ | ______ | ______ |
| (x, y) | (0, −9) | (______, _______) | (______, _______) | ______ |
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`
Solve: 99x + 101y = 499, 101x + 99y = 501
The length of the rectangle is 5 more than twice its breadth. The perimeter of a rectangle is 52 cm, then find the length of the rectangle
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?
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.
