Question

How do you solve `2x + 7y = 30` and `x = 48 - 9y` using substitution?

Answer 1

`y = 6`

Explanation:

`2x + 7y = 30 " " and " " color(red)(x = 48 - 9y)`

Remember that the = sign tells us that two expressions are absolutely the same as each other - specifically that they are inter-changeable! In these equations: `"x IS THE SAME AS (48 - 9y)"`.

So, in the first equation an `x` can be replaced by (48 - 9y).

`2color(red)x + 7y = 30 " " rArr 2color(red)((48 - 9y)) + 7y = 30`

`2(48 - 9y) + 7y = 30`
`96 - 18y + 7y = 30`
`96 - 30 = 18y - 7y`

`66 = 11y`

`6 = y`