Question: To solve:

Solution:

Let the first equation be Eq(1), and let the second equation be Eq(2).

To make solving easier, let's consider that:

Substitute these values in the two equations given in the question.

For equation 1:

Let the above equation be named Eq(3).

For equation 2:

Let the above equation be named Eq(4).

On observing both the equations 3 and 4, you can tell that they're of the form;

ax + by = c₁

bx + AY = c₂

When equations are of this form, we can USE the Add & Subtract Method to solve them.

[Any other method is fine too, this one's quicker for these kind of questions]

Adding equations (3) and (4) we get:

⇒ 32a + 33b + [33a + 32b] = 31 + [34]

⇒ 65a + 65b = 65

⇒ 65[a + b] = 65

⇒ a + b = 1 → Let this be Eq(5)

Subtracting equations (3) and (4) we get:

⇒ 32a + 33b - [33a + 32b] = 31 - 34

⇒ 32a + 33b - 33a - 32b = -3

⇒ -a + b = -3 → Let this be Eq(6)

Now, on adding Eq(5) and Eq(6) we get:

⇒ a + b + [-a + b] = 1 + [-3]

⇒ a + b - a + b = 1 - 3

⇒ 2b = -2

⇒ b = -1

Substitute the VALUE of "b" in Eq(6).

⇒ -a + b = -3

⇒ -a + [-1] = -3

⇒ -a - 1 = -3

⇒ -a = -3 + 1

⇒ -a = -2

⇒ a = 2

Now we've got the values of both "a" and "b". Now substitute both "a" and "b" in 1/x = a and 1/y = b RESPECTIVELY,

For 'x':

For 'y':

Therefore:

x = 1/2

y = -1

Hence solved.