(x)/(4) - (3)/(8)y = 3 \\ (5)/(3)x - (y)/(2) = 12 How to solve the following simultaneous pair of equation by substitution both. ​

Question

`(x)/(4) - (3)/(8)y = 3 \\`


`(5)/(3)x - (y)/(2) = 12`
How to solve the following simultaneous pair of equation by substitution both. ​

Answer 1

(6, - 4 )

Explanation:

Given the 2 equations

`(x)/(4)` -
`(3)/(8)` y = 3 → (1)

`(5)/(3)` x -
`(y)/(2)` = 12 → (2)

Multiply (1) by 8 and (2) by 6 to clear the fractions

2x - 3y = 24 → (3)

10x - 3y = 72 → (4)

Rearrange (3) expressing - 3y in terms of x by subtracting 2x from both sides

- 3y = 24 - 2x

Substitute 3y = 24 - 2x into (4)

10x + 24 - 2x = 72, that is

8x + 24 = 72 ( subtract 24 from both sides )

8x = 48 ( divide both sides by 8 )

x = 6

Substitute x = 6 in either (3) or (4) and solve for y

Substituting in (3)

2(6) - 3y = 24

12 - 3y = 24 ( subtract 12 from both sides )

- 3y = 12 ( divide both sides by - 3 )

y = - 4

Solution is (6, - 4 )