Question

How do you solve the system `y=4x; 2y-x=16`?

Answer 1

See full solution process below

Explanation:

Step 1) Because the first equation is already solved for `y` we can substitute `4x` for `y` in the second equation and solve for `x`:

`(2 xx 4x) - x = 16`

`8x - x = 16`

`8x - 1x = 16`

`(8 - 1)x = 16`

`7x = 16`

`(7x)/color(red)(7) = 16/color(red)(7)`

`(color(red)(cancel(color(black)(7)))x)/cancel(color(red)(7)) = 16/7`

`x = 16/7`

Step 2) We can now substitute `16/7` for `x` in the first equation and calculate `y`:

`y = 4 xx 16/7`

`y = 64/7`

The solution is:

`x = 16/7` and `y = 64/7`