Question

Is (5, -1) a solution to this system of equations: `3x+6y = 9` and `-2x-y = -6` ?

Answer 1

No. See below, the second equation is not solve therefore this point is not a solution for this set of equations.

Explanation:

To determine if this point is a solution to the system of equations we need to substitute the point into each equation and see if it solves the equation.

We will substitute `color(red)(5)` for `color(red)(x)` and `color(blue)(-1)` for `color(blue)(y)`

Then `3color(red)(x) + 6color(blue)(y) = 9` becomes:

`(3 xx color(red)(5)) + (6 xx color(blue)(-1)) = 9`

`15 - 6 = 9`

`9 = 9`

And `-2color(red)(x) - color(blue)(y) = -6` becomes:

`(-2 xx color(red)(5)) - (color(blue)(-1)) = -6`

`-10 + = -6`

`-9 != -6`

Because the second equation is not solve this point is not a solution for this set of equations.