Advertisements
Advertisements
Question
By equating coefficients of variables, solve the following equation.
x − 2y = −10 ; 3x − 5y = −12
Advertisements
Solution
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
RELATED QUESTIONS
Solve the following system of linear equations by applying the method of elimination by equating the coefficients
(i)4x – 3y = 4
2x + 4y = 3
(ii)5x – 6y = 8
3x + 2y = 6
Solve the following system of equations: 15x + 4y = 61; 4x + 15y = 72
Solve the following system of linear equations :
2(ax – by) + (a + 4b) = 0
2(bx + ay) + (b – 4a) = 0
Solve the following pair of linear equation by the elimination method and the substitution method.
3x – 5y – 4 = 0 and 9x = 2y + 7
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?
Ajay is younger than Vijay by 5 years. Sum of their ages is 25 years. What is Ajay's age?
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 - 2y = -1 ; 2x - y = 7
Solve the following simultaneous equation.
2x - y = 5 ; 3x + 2y = 11
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.
5x + 7y = 17 ; 3x - 2y = 4
Difference between two numbers is 3. The sum of three times the bigger number and two times the smaller number is 19. Then find the numbers
The semi perimeter of a rectangular shape garden is 36 m. The length of the garden is 4 m more than its breadth. Find the length and the breadth of the garden
The ratio of two numbers is 2:3. If 5 is added in each numbers, then the ratio becomes 5:7 find the numbers.
The ratio of two numbers is 2:3.
So, let the first number be 2x and the second number be `square`.
From the given condition,
`((2x) + square)/(square + square) = square/square`
`square (2x + square) = square (square + square)`
`square + square = square + square`
`square - square = square - square`
`- square = - square`
x = `square`
So, The first number = `2 xx square = square`
and, Second number = `3 xx square = square`
Hence, the two numbers are `square` and `square`
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.
