Question

How do you solve the system `y=3x` and `2x+y=15` using substitution?

Answer 1

See a solution process below:

Explanation:

Step 1) Because the first equation is already solved for `y` we can substitute `3x` for `y` in the second equation and solve for `x`:

`2x + y = 15` becomes:

`2x + 3x = 15`

`(2 + 3)x = 15`

`5x = 15`

`(5x)/color(red)(5) = 15/color(red)(5)`

`(color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5)) = 3`

`x = 3`

Step 2) Substitute `3` for `x` in the first equation and calculate `y`:

`y = 3x` becomes:

`y = 3 xx 3`

`y = 9`

The solution is: `x = 3` and `y = 9` or `(3, 9)`