Question

Plz help
Topic: Simultaneous equations
Class 9 ICSE​

Answer 1

19 and 13

Explanation:

Let x be the larger number and y the smaller , then

`(3x)/(y)` = 4 +
`(5)/(y)` ( multiply through by y to clear the fractions )

3x = 4y + 5 ( subtract 4y from both sides )

3x - 4y = 5 → (1)

and

`(6y)/(x)` = 4 +
`(2)/(x)` ( multiply through by x to clear the fractions )

6y = 4x + 2 ( subtract 4x from both sides )

- 4x + 6y = 2 → (2)

Multiplying (1) by 4 and (2) by 3 and adding will eliminate x

12x - 16y = 20 → (3)

- 12x + 18y = 6 → (4)

Add (3) and (4) term by term to eliminate x

0 + 2y = 26

2y = 26 ( divide both sides by 2 )

y = 13

Substitute y = 13 into (1) and solve for x

3x - 4(13) = 5

3x - 52 = 5 ( add 52 to both sides )

3x = 57 ( divide both sides by 3 )

x = 19

The 2 numbers are 19 and 13