To answer this question, we need to remember that the linear combination method is a process in which we can add two equations in a way that one of the variables is eliminated, and, therefore, we can solve the equation for the other variable.
In this case, we have:
[tex]\begin{cases}6g+8h=40 \\ -6g+2h=-20\end{cases}[/tex]
If we add both equations, we have:
[tex]\begin{gathered} \frac{\begin{cases}6g+8h=40 \\ -6g+2h=-20\end{cases}}{0g+10h=20} \\ 10h=20 \\ \frac{10}{10}h=\frac{20}{10} \\ h=2 \end{gathered}[/tex]
Then we can substitute this value of h in one of the original equations to find g:
[tex]\begin{gathered} 6g+8(2)=40 \\ 6g+16=40 \\ \end{gathered}[/tex]
And to solve this equation, we can subtract 16 from both sides of the equation, and then divide both sides by 6:
[tex]\begin{gathered} 6g+16-16=40-16 \\ 6g=24 \\ \frac{6g}{6}=\frac{24}{6} \\ g=4 \end{gathered}[/tex]
In summary, therefore, we have that the values are:
• g = 4
,
• h = 2
