Question

How do you solve the system of equations `y= - 2x + 6` and `2y + x = - 5`?

Answer 1

See the entire solution process below:

Explanation:

Step 1) Because the first equation is already solved for `y` we can substitute `-2x + 6` for `y` in the second equation and solve for `x`:

`2y + x = -5` becomes:

`2(-2x + 6) + x = -5`

`(2 xx -2x) + (2 xx 6) + x = -5`

`-4x + 12 + x = -5`

`-4x + x + 12 = -5`

`-3x + 12 = -5`

`-3x + 12 - color(red)(12) = -5 - color(red)(12)`

`-3x + 0 = -17`

`-3x = -17`

`(-3x)/color(red)(-3) = (-17)/color(red)(-3)`

`(color(red)(cancel(color(black)(-3)))x)/cancel(color(red)(-3)) = 17/3`

`x = 17/3`

Step 2) Subsitute `17/3` for `x` in the first equation and calculate `y`:

`y = -2x + 6` becomes:

`y = -34/3 + (3/3 xx 6)`

`y = -34/3 + 18/3`

`y = -16/3`

The solution is: `x = 17/3` and `y = -16/3` or `(17/3, -16/3)`