Question

solving systems with subtraction

Answer 1

We have the following system of linear equations:

$\begin{gathered} y-5=x \\ x=-2-y \end{gathered}$

We can take the first equation, and express y in terms of x:

$y=x+5$

Now we can plugin y in the second equation and solve for x:

$\begin{gathered} x=-2-(x+5) \\ x=-2-x-5 \\ x+x=-2-5 \\ 2x=-7 \\ x=-\frac{7}{2} \end{gathered}$

We take the first equation y = x+5, replace x and find y:

$\begin{gathered} y=-\frac{7}{2}+5 \\ y=\frac{3}{2} \end{gathered}$

Answer: (-7/2, 3/2)