Question

How do you solve the system `4x-5y=-7` and `y=5x` using substitution?

Answer 1

`x = 1/3 and y = 5/3`

Explanation:

There are two variables, therefore we need two equations.

`4x-5y=-7` and `color(red)(y=5x)`

`color(red)(y=5x)` means that `y and 5x` have exactly the same value.

`color(red)(y" and " 5x)` are therefore interchangeable.

`4x-5color(red)(y)=-7` has two variables and therefore cannot be solved with one unique solution. There are infinitely many answers.

Replace `color(red)(y)` by `color(red)(5x)`
This gives an equation with only ONE variable and it can be solved.

`" "4x-5color(red)(y)=-7`
`color(white)(xxxxxxx)darr`
`rarr4x-5color(red)((5x))=-7" "` (now the equation has only x)

`4x -25x = -7`

`-21x = -7" "larr div -21`

`x = 1/3`

Now find the value of `y`, knowing that `y = 5x`

`y = 5(1/3)`

`y = 5/3`