Question

For the linear equation, find the product of 5 and the linear equation, and solve both equations for y. 2x + 7y = 11

Answer 1

(a)
`10x + 35y = 55`

(b)
`y = (11 - 2x)/(7)`

Explanation:

Given

`2x + 7y = 11`

Solving (a): Multiply equation by 5.

Multiply both sides by 5

`5 * (2x + 7y) = 11*5`

Open bracket

`5 * 2x + 5 * 7y = 11*5`

`10x + 35y = 55`

(b) Solve for y in
`10x + 35y = 55` and
`2x + 7y = 11`

`10x + 35y = 55`

Subtract 10x from both sides

`35y = 55 - 10x`

Divide both sides by 35

`(35y)/(35) = (55 - 10x)/(35)`

`y = (55 - 10x)/(35)`

Factorize the numerator:

`y = (5(11 - 2x))/(35)`

Express 35 as 7 * 5

`y = (5(11 - 2x))/(7 * 5)`

`y = ((11 - 2x))/(7)`

`y = (11 - 2x)/(7)`

When
`2x + 7y = 11` is solved, the solution will be:
`y = (11 - 2x)/(7)`