Answer:
![constant\rightarrow-4](https://img.qammunity.org/2023/formulas/mathematics/college/ufvdev9phh202nv07o0jb67maq8nqs90xu.png)
Step-by-step explanation: We have to find the constant that when multiplied to the first equation and added to the second, the variable x gets canceled out, the two equations are as follows:
![\begin{gathered} x+2y=2\rightarrow(1) \\ 4x-5y=8\rightarrow(2) \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/899zb53b4ieidjfygfmrmw7vb4z8onk36z.png)
Multiplying the equation (1) by -4 and adding it to the equation (2) gives the following answer:
![\begin{gathered} -4*(x+2y)=-4*2\rightarrow-4x-8y=-8 \\ \begin{equation*} -4x-8y=-8 \end{equation*} \\ + \\ \begin{equation*} 4x-5y=8 \end{equation*} \\ ---------------------- \\ -3y=0 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/utvy68vlgpt33drt7hgzw2vnr80smypl4u.png)
Therefore the value of the constant is -4.