Advertisements
Advertisements
प्रश्न
By equating coefficients of variables, solve the following equation.
4x + y = 34 ; x + 4y = 16
उत्तर
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
संबंधित प्रश्न
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
Two types of boxes A, B are to be placed in a truck having a capacity of 10 tons. When 150 boxes of type A and 100 boxes of type B are loaded in the truck, it weighes 10 tons. But when 260 boxes of type A are loaded in the truck, it can still accommodate 40 boxes of type B, so that it is fully loaded. Find the weight of each type of box.
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?
Solve the following simultaneous equation.
2x + y = -2 ; 3x - y = 7
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 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 angles of a cyclic quadrilateral ABCD are ∠A = (6x + 10)°, ∠B = (5x)°, ∠C = (x + y)°, ∠D = (3y – 10)°. Find x and y, and hence the values of the four angles.
Evaluate: (1004)3
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`
