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

Mar 22, 2018

This is a system of simultaneous equations.

$y = - 7$

Explanation:

Call the two equations:

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

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:

$y = - 2 \left(1 - y\right) + 9$

Multiply out the parentheses:

$y = - 2 + 2 y + 9$

Collect like terms (which involves subtracting $2 y$ 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.