Question

find value of x andy using shortcut
110x + 125y = 105000 and 125x + 110y = 106500​

Answer 1

Answer:

x = 500

y = 400

Step-by-step explanation:

110x + 125y = 105000

or

22x + 25y = 21000 .....(i)

125x + 110y = 106500

or

25x + 22y = 21300 ....(ii)

subtract eq (i) from (ii)

{25x + 22y} - {(22x + 25y)} = 21300 - 21000

=> 25x - 22x + 22y - 25y = 300

=> 3x - 3y = 300

=> x - y = 100

=> x = 100 + y.....(iii)

putting this value of x in eq (i)

we get

22x + 25y = 21000

=> 22(100 + y) + 25y = 21000

=> 2200 + 22y + 25y = 21000

=> 47y = 21000 - 2200

=> y = 18800/47

=> y = 400

so

x = 100 + y = 100 + 400 = 500

Answer 2

Answer:

X=500, Y=400

Step-by-step explanation:

110x + 125y = 105000

22x + 25y =21000........eqn (1)

125x + 110y = 106500

25x + 22y = 21300.......eqn (2)

In Equation (1) & (2) the coefficients of x and y are different

(a) To make the coefficients of x same we need to multiply equation (1) by 25 and Equation (2) by 22

(b) To make the coefficients of y same we need to multiply equation (1) by 22 and Equation (2) by 25

Lets keep coefficient of x same in both equation

22x + 25y =21000........eqn (1). X 25

25x + 22y = 21300.......eqn (2). X 22

Let it be equation 3 & 4

550x + 625y =525000......eqn (3)

550x + 484y =468600.......eqn (4)

Solving the equation 3 & 4 we get Y=400

Now, substitute the value of Y in any of the above equation

We get X=500