Question

How do you solve the following linear system: `3x + y = 4 , x = 5y + 2`?

Answer 1

See a solution process below:

Explanation:

Step 1) Because the second equation is already solved for `x` we can substitute `(5y + 2)` for `x` in the first equation and solve for `y`:

`3x + y = 4` becomes:

`3(5y + 2) + y = 4`

`(3 xx 5y) + (3 xx 2) + y = 4`

`15y + 6 + y = 4`

`15y + 6 - color(red)(6) + y = 4 - color(red)(6)`

`15y + 0 + y = -2`

`15y + y = -2`

`15y + 1y = -2`

`(15 + 1)y = -2`

`16y = -2`

`(16y)/color(red)(16) = -2/color(red)(16)`

`(color(red)(cancel(color(black)(16)))y)/cancel(color(red)(16)) = -2/16`

`y = -1/8`

Step 2) Substitute `-1/8` for `y` in the second equation and calculate `x`:

`x = 5y + 2` becomes:

`x = (5 xx -1/8) + 2`

`x = -5/8 + (8/8 xx 2)`

`x = -5/8 + 16/8`

`x = (-5 + 16)/8`

`x = 11/8`

The Solution Is:

`x = 11/8` and `y = -1/8`

Or

`(11/8, -1/8)`