Question

27x 31y = 85 ; 31x 27y =89

Answer 1

x = 2 and y = 1

Step-by-step explanation:

We have,

27x + 31y = 85              ......(1)

31x + 27y = 89             ......(2)

To find, the values of x and y=

By substitution method,

From (1),

27x + 31y = 85

⇒ 27x = 85 - 31y

⇒ $x=\dfrac{85-31y}{27}$    ..... (A)

Put $x=\dfrac{85-31y}{27}$ in (2), we get

$31(\dfrac{85-31y}{27})+27y=89$

⇒$\dfrac{2635-961y+729y}{27}=89$

⇒ $2635-232y=89\times 27=2403$

⇒$-232y=2403-2635=-232$

⇒ y = 1

Put y = 1 in (A), we get

$x=\dfrac{85-31}{27}=\dfrac{54}{27}$

⇒ x = 2

Hence, x = 2 and y = 1

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Answer 2

Given: 27x + 31y = 85 and 31x + 27y = 89

To find: the value of x and y

Solution:

When the value of the coefficient of x and y are interchanged, we use the Substitution Method to find the value of x and y.

The strategy for substitution includes three stages:

1. Tackle one condition for one of the factors.
2. Substitute (plug-in) this expression into the other condition and tackle.
3. Resubstitute the worth into the first condition to see as the comparing variable.

Therefore, 27x + 31y = 85

              => x = (85 - 31y)/27   ___(1)

Putting equation (1) in 31x + 27y = 89,

=> 31 (85 - 31y) / 27 + 27y = 89

=> 2635 - 961y + 729y = 89 x 27 = 2403

=> -232y = -232

=> y = 1    ____(2)

Putting equation (2) in (1),

=> x = (85 - 31(1) ) / 27

=> x = 54/27

=> x = 2

Thus the value of x and y are 2 and 1 respectively.