How do you solve this system of equations by substitution: `x+ 4y = - 14 and y = 2x - 8`?

We're given `y=2x-8.` This means that we can replace all instances of `y` in the first equation with `2x-8.` The goal when given a system of equations in two variables is two get an equation with one variable and solve for that variable, and subsequently back-substitute your solution in to get the other variable.

`x+4(2x-8)=-14`

`x+8x-32=-14`

Solve for `x:`

`9x-32=-14`

`9x=18`

`x=2`

To solve for `y,` simply plug in `x=2` into `y=2x-8.`

`y=2(2)-8=-4`

So, the solution is

`(x, y)=(2, -4)`

Step 1) Because the second equation is already solve for `y` we can substitute `(2x - 8)` for `y` in the first equation and solve for `x`:

`x + 4y = -14` becomes:

`x + 4(2x - 8) = -14`

`x + (4 xx 2x) - (4 xx 8) = -14`

`x + 8x - 32 = -14`

`1x + 8x - 32 = -14`

`(1 + 8)x - 32 = -14`

`9x - 32 = -14`

`9x - 32 + color(red)(32) = -14 + color(red)(32)`

`9x - 0 = 18`

`9x = 18`

`(9x)/color(red)(9) = 18/color(red)(9)`

`(color(red)(cancel(color(black)(9)))x)/cancel(color(red)(9)) = 2`

`x = 2`

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

`y = 2x - 8` becomes:

`y = (2 xx 2) - 8`

`y = 4 - 8`

`y = -4`

The Solution Is:

`x = 2` and `y = -4`

Or

`(2, -4)`