Answer:
[tex]constant\rightarrow-4[/tex]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:
[tex]\begin{gathered} x+2y=2\rightarrow(1) \\ 4x-5y=8\rightarrow(2) \end{gathered}[/tex]Multiplying the equation (1) by -4 and adding it to the equation (2) gives the following answer:
[tex]\begin{gathered} -4\times(x+2y)=-4\times2\rightarrow-4x-8y=-8 \\ \begin{equation*} -4x-8y=-8 \end{equation*} \\ + \\ \begin{equation*} 4x-5y=8 \end{equation*} \\ ---------------------- \\ -3y=0 \end{gathered}[/tex]Therefore the value of the constant is -4.
