Answer
The systems of equations are $x+y=2$ and $x-y=8$ and the solution to the equations is $\left( x,y \right)=\left( 5,-3 \right)$.
Work Step by Step
Let us assume the two numbers are x and y.
And the sum of the numbers is 2. This gives the equation as:
$x+y=2$
And the difference between the numbers is −1. This gives the equation as:
$x-y=8$
Add equations $x+y=2$ and $x-y=8$ to obtain:
$\begin{align}
& x+y+x-y=2+8 \\
& 2x=10 \\
& x=5
\end{align}$
Substitute the value of x in equation (I)
$\begin{align}
& 5+y=2 \\
& y=-3
\end{align}$
Hence, the system of equations are $x+y=2$ and $x-y=8$ and the solution to the system of equations is $\left( x,y \right)=\left( 5,-3 \right)$.
