Question

•solve 17 number question by using substitution or elimination method...​

Answer 1

Answer:

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Answer 2

Answer:-

• x = 6
• y = 4

Given:-

▶ 40 / (x + y) + 2 / (x - y) = 5

▶ 25 / (x + y) - 3 / (x - y) = 1

We have to solve the question either by substitution or elimination method. For sake of simplicity, Let's solve the question using elimination. But first,

• The two variables are in denominator, So It would involve a lot of calculation. Hence, We should convert it into simpler form.

Let 1 / (x + y) = a & 1 / (x - y) = b

The equation becomes,

⇒ 40a + 2b = 5 ...(1)

and,

⇒ 25a - 3b = 1 ...(2)

Multiply, (1) by 3 and (2) by 2.

⇒ 120a + 6b = 15 ...(3)

⇒ 50a - 6b = 2 ...(4)

Adding (3) and (4), we get (Elimination method)

⇒ 120a + 6b + 50a - 6b = 15 + 2

⇒ 170a = 17

⇒ a = 1 / 10 ...(5)

Substitute value of a in eq(1),

⇒ 40×1/10 + 2b = 5

⇒ 4 + 2b = 5

⇒ 2b = 1

⇒ b = 1 / 2

But, a = 1 / (x + y) & b = 1 / (x - y),

So,

⇒ a = 1 / (x + y)

⇒ 1 / 10 = 1 / (x + y)

⇒ x + y = 10 ...(6)

Also,

⇒ b = 1 / (x - y)

⇒ 1 / 2 = 1 / (x - y)

⇒ x - y = 2 ...(7)

Using elimination method for (6) & (7),

x + y = 10

x - y = 2

________

2x = 12

~~~~~~~~~

∴ x = 6

Substituting value of x in eq(6), we get

⇒ x + y = 10

⇒ y = 10 - 6

⇒ y = 4

Hence, The value of [ x is 6 ] and [ y is 4 ]