We have the following system of equations:
[tex]\begin{gathered} 3x+y=4 \\ 2x+y=5 \end{gathered}[/tex]The linear combintation method is a process of adding two algebraic equations so that one od the variables is eliminated.
In this regard, by multiplying the second equation by -1, we obtain an equivalent system of equations:
[tex]\begin{gathered} 3x+y=4 \\ -2x-y=-5 \end{gathered}[/tex]Then, by adding both equations, we can eliminate the variable y, that is,
[tex]\begin{gathered} 3x-2x+y-y=4-5 \\ \text{which gives} \\ x=-1 \end{gathered}[/tex]Once we know the result for x, we can substitute its values into one of the orginal equations. Then, if we substitute x=-1 into the first equation, we have
[tex]3(-1)+y=4[/tex]which gives
[tex]\begin{gathered} -3+y=4 \\ \text{then} \\ y=7 \end{gathered}[/tex]Therefore, the solution is ( -1, 7), which corresponds to the last option.
