Solve the system of equations by either the addition method or the subtitution method. Express numbers as integers or decimals. displaystyle-{0.1}{x}+{0.1}{y}={0.2} displaystyle{0.1}{x}+{0.1}{y}={0.1}

Step 1
Consider the give system of the equations as ${\displaystyle \{\begin{array}{c}-0.1x+0.1y=0.2\\ 0.1x+0.1y=0.1\end{array}}$ .
Multiply the system of equation by 10 on each sides and obtained as system of the equations as ${\displaystyle \{\begin{array}{c}-x+y=2\\ x+y=1\end{array}}$.
Step 2
Solve the above equations using addition method as follows.
${\displaystyle -x+y=2}$
${\displaystyle \frac{x+y=1}{0+2y=3}}$
${\displaystyle y=\frac{3}{2}}$
$y=1.5$
Step 3
Substitute $y=1.5$ in the first equation and solve for y as follows.
${\displaystyle -x+1.5=2}$
${\displaystyle -x=2-1.5}$
$x=-0.5$
Thus, the solution set of the given equations is $(-0.5,1.5).$