Respuesta :
Answer:
[tex]h=2[/tex] and [tex]g=4[/tex]
Step-by-step explanation:
In the combination method, both equations are added or subtracted so that a variable is eliminated and it is possible to determine the value of the remaining variable.
We have the equations:
[tex]6g+8h=40[/tex]
[tex]-6g+2h=-20[/tex]
In this case, if we add the two equations given, g will be eliminated and we could find the value of h.
- Adding the equations:
[tex]6g+8h=40\\+(-6g+2h=-20)[/tex]
----------------------------------
[tex]6g+(-6g)+8h+(+2h)=40+(-20)\\=6g-6g+8h+2h=40-20\\0g+10h=20\\10h=20\\h=\frac{20}{10} =2[/tex]
We have [tex]h=2[/tex], Now we only need [tex]g[/tex], so we substitute the value of [tex]h[/tex] in any of the original equations:
[tex]6g+8h=40[/tex]
since [tex]h=2[/tex]
[tex]6g+8(2)=40[/tex]
[tex]6g+16=40[/tex]
[tex]6g=40-16[/tex]
[tex]6g=24[/tex]
[tex]g=\frac{24}{6} =4[/tex]
so the answer is [tex]h=2[/tex] and [tex]g=4[/tex]
