Linear Equations in Two Variables Test - 4

x = 3 and y = 5
(p - 1)3 + (2p - 5)5 = 11
3p - 3 + 10p - 25 = 11
3p + 10p = 11 + 25 + 3
13p = 39
p = 3

x + (2k)y + 13 = 0 and C(3, 4)

Using x = 3 and y = 4,
3 + (2k)4 + 13 = 0
3 + 8k + 13 = 0
8k = -16
k = -2

The value of k will be -2.

Let the number of adult tickets sold be x and the number of child tickets sold be y.

Total number of tickets sold = 500
x + y = 500
⇒ y = 500 - x

According to the question:
3x + 2y = 1300
3x + 2(500 - x) = 1300

3x + 1000 - 2x = 1300
x + 1000 = 1300

x = 1300 - 1000 = 300

So, number of adult tickets sold = 300

Number of child tickets sold = y = 500 - x
= 500 - 300
= 200

x - 8y = 12
Let x = 4 and y = -1
4 - (8 (-1)) = 12
4 + 8 = 12
12 = 12
Therefore, the co-ordinates of this point satisfy the equation.

7x + 4y = 18 … (1)
Now, x - y = 0
Or x = y

Put x = y in equation (1).
7y + 4y = 18
11y = 18

Now, x = y
11x = 11y = 18

Now, 11(x + y) = 11x + 11y
= 18 + 18
= 36

x and y are non-negative integers. (Given)
Start from x = 0.

If x = 0, 1, or 2, y cannot be an integer.
For x = 3, y = 3
And for x = 7, y = 0

These two pairs only satisfy the given equation.

Given that population of city A be x and that of city B be y.

(1)
A.T.Q, 3y - 7,00,000 = x
3y = x + 7,00,000
(2)
If population of city A is x = 8,00,000

A.T.Q,

3y - 7,00,000 = x
3y - 7,00,000 = 8,00,000
3y = 7,00,000 + 8,00,000
3y = 15,00,000
y = 15,00,000 ÷ 3
y = 5,00,000

Therefore, population of city B: (y) = 5,00,000

Difference between the population of city A and city B = 8,00,000 - 5,00,000 = 3,00,000