Question

How do I find the Y coordinate? `y = -2x+9` and `-x-y=-1`

Answer 1

This is a system of simultaneous equations.

`y=-7`

Explanation:

Call the two equations:

Equation 1: `y=-2x+9`

Equation 2: `-x-y=-1`

Multiply both sides of Equation 2 by `-1`:

`x+y=1`

Subtract `y` from both sides:

`x=1-y`

Now, we can substitute this value of `x`, in terms of `y`, into Equation 1 where we see `x` in it:

`y=-2(1-y)+9`

Multiply out the parentheses:

`y=-2+2y+9`

Collect like terms (which involves subtracting `2y` from both sides):

`-y=7`

Multiply both sides by `-1`:

`y=-7`

We could also solve to find the value of `x`, but we are not asked to do so.

It's worthwhile and interesting to realise that these two equations are the equations of straight lines, and the `x` and `y` values in the solution are the coordinates of the point where the two straight lines cross.