Question

How do you solve the system of equations `x+ 2y = 1` and `6x = - 16- 12y`?

Answer 1

See a solution process below:

Explanation:

Step 1) Solve the first equation for `x`:

`x + 2y = 1`

`x + 2y - color(red)(2y) = 1 - color(red)(2y)`

`x + 0 = 1 - 2y`

`x = 1 - 2y`

Step 2) Substitute `(1 - 2y)` for `x` in the second equation and solve for `y`:

`6x = - 16 - 12y` becomes:

`6(1 - 2y) = - 16 - 12y`

`(6 * 1) - (6 * 2y) = - 16 - 12y`

`6 - 12y = - 16 - 12y`

`6 - 12y + color(red)(12y) = - 16 - 12y + color(red)(12y)`

`6 - 0 = - 16 - 0`

`6 != -16`

Because `6` obviously is not equal yto `-16` there is not solution to this problem. Or, the solution is the null or empty set: `{O/}`

What this indicates is the two lines these equations represent are parallel and are not different equations for the same line. By definition of being parallel, parallel lines never intersect.