Answer:
![PO=86.2\\ OM=23.8\\](https://img.qammunity.org/2021/formulas/mathematics/college/z13lojxn2xru8yjm8jvu4vet6e8v5ldpxa.png)
Explanation:
To preface, your figure is going to be a line segment, with
as your midpoint, in between points
&
![M.](https://img.qammunity.org/2021/formulas/mathematics/college/j6gg9i8hc095hzb5hxkl81yrd4ik7ns9f4.png)
With that being said:
![PO+OM=PM](https://img.qammunity.org/2021/formulas/mathematics/college/1wxu5l3d0vlip6ny9t11g9hqc7juestq1o.png)
Identify your values:
![PO=7y+12\\OM=3y-8\\PM=110](https://img.qammunity.org/2021/formulas/mathematics/college/ellv0xfwrg6ti1dbzr9c73ycr17djtnxs4.png)
Substitute the values into the first equation:
![7y+12+3y-8=110](https://img.qammunity.org/2021/formulas/mathematics/college/rrhv6dv3fqhrejnsi9fpt8xeq11b0viohj.png)
Combine like terms:
![10y+4=110](https://img.qammunity.org/2021/formulas/mathematics/college/jyeym4jthzxzxncubzvg1qy10g4uhlfbdk.png)
Subtract
from both sides of the equation:
![10y=106](https://img.qammunity.org/2021/formulas/mathematics/college/rijsuaix4qj4483y7ac5l0odl7bejnpp6m.png)
Divide by the coefficient of
, which is
:
![y=10.6](https://img.qammunity.org/2021/formulas/mathematics/college/xrrkphc40f5s5dgttoymes6uvb4ger1w7m.png)
Substitute
for
in segments
&
:
![PO=7(10.6)+12](https://img.qammunity.org/2021/formulas/mathematics/college/wbud4m3jfxsam80nfbkz05hjuqf1n0a5fz.png)
![OM=3(10.6)-8](https://img.qammunity.org/2021/formulas/mathematics/college/ekdlqoksmwspjtqtzhh2cwgmh5du2pwd3t.png)
![PO=74.2+12](https://img.qammunity.org/2021/formulas/mathematics/college/580jxc6cknrisei1ypy8cxxko7jmw37nt0.png)
![OM=31.8-8](https://img.qammunity.org/2021/formulas/mathematics/college/6ehazkol4ju5w3mu25wjhvmfxpt5d3ftxo.png)
Solve:
![PO=86.2](https://img.qammunity.org/2021/formulas/mathematics/college/j7f82s081j5j3adax0nefgyc12h0l43uuk.png)
![OM=23.8](https://img.qammunity.org/2021/formulas/mathematics/college/nun8ggblgjl6qhlvpceusiprovoj5fjzls.png)
Check your answers by substituting:
![PO+OM=PM](https://img.qammunity.org/2021/formulas/mathematics/college/1wxu5l3d0vlip6ny9t11g9hqc7juestq1o.png)
![86.2+23.8=110](https://img.qammunity.org/2021/formulas/mathematics/college/ccwwskwfpdjncf1ge6ts991k8hinu9032q.png)