If 173x + 197y = 149 and 197x + 173y = 221, then find (x, y)

If an ordered pair satisfying the equations 2x – 3y = 18 and 4x – y = 16 also satisfies the equation 5x-py-23 = 0, then find the value of ‘p’.

In a fraction, if the numerator is decreased by 1 and the denominator is increased by 1, then the fraction becomes $\frac{1}{2}\mathrm{.}\backslash frac\{1\}\{2\}.$ Instead, if the numerator is increased by 1 and the denominator is decreased by 1, then the fraction becomes $\frac{4}{5}\mathrm{.}\backslash frac\{4\}\{5\}.$ Find the numerator of the fraction.

If $a_{1}x+b_{1}y+c_1=0a\_1\; x\; +\; b\_1\; y\; +\; c\; \_1=\; 0$ and $a_{2}x+b_{2}y+c_2=0a\_2\; x\; +\; b\_2\; y\; +\; c\_2\; =\; 0$ are such that $a_1,b_1,c_1,a_2,b_{2}a\_1\; ,\; b\_1\; ,\; c\_1\; ,\; a\_2\; ,\; b\_2$ and $c_{2}c\_2$ are consecutive integers in the same order then find the values of x and y.

If the ordered pair (sinθ, cosθ) satisfies the system of equations mx + ny + a + b = a-b and nx + my + 2b = 0, then find the value of ‘θ’ where 0 ≤ θ ≤, 90° (m ≠ n)

If we increase the length by 2 units and the breadth by 2 units, then the area of rectangle is increased by 54 square units. Find the perimeter of the rectangle (in units).

A two-digit number is formed by either subtracting 17 from nine times the sum of the digits or by adding 21 to 13 times the difference of the digits. Find the number.

If 3|x| + 5|y| = 8 and 7|x| - 3|y| = 48, then find the value of x + y.

A, B, C and D share a certain amount amongst themselves. B sees that the other three get 3 times what he himself gets, C sees that the other three get 4 times what he gets, while D sees that the other three get 5 times what he gets. If the sum of the largest and smallest shares is 99, then what is the sum of the other two shares ?

The total cost of six books, five pencils and seven sharpeners is Rs. 115 and that of eight books, ten pencils and fourteen sharpeners is Rs. 190. Then which of the following article’s cost can be found uniquely