Y=-x-1 y=-2x+1 ?

Mar 9, 2018

$2 = x$

Explanation:

Substitute the $- x - 1$ for $y$ to get

$- x - 1 = - 2 x + 1$

Add $x$ to $- x$ and $- 2 x$ to get

$- 1 = - 1 x + 1$

Subtract $1$ from $1$ and $- 1$ to get

$- 2 = - 1 x$

Divide both sides by $- 1$ to get

$2 = x$

Mar 9, 2018

Linear algebra states that x=2, making y=-3

Explanation:

Linear algebra allows us to add and subtract whole equations from each other, like so:

$y = - 2 x + 1$
$-$
$\underline{y = - x - 1}$
$0 = - x + 2$

Taking the solution from the bit of linear algebra we've done:
$0 = - x + 2 \Rightarrow \textcolor{red}{x = 2}$

We can now plug our solution for $x$ back into either of the equations and solve for $y$:

$y = - \left(2\right) - 1 \Rightarrow y = - 2 - 1 \Rightarrow \textcolor{red}{y = - 3}$
$y = - 2 \left(2\right) + 1 \Rightarrow y = - 4 + 1 \Rightarrow \textcolor{red}{y = - 3}$