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We have
[tex]\begin{gathered} 3x+y=10 \\ 4x-y=4 \end{gathered}[/tex]we will use the elimination method to sum the first equation with the second equation
[tex]\begin{gathered} 3x+4x+y-y=10+4 \\ 7x=14 \end{gathered}[/tex]then we can isolate the x
[tex]\begin{gathered} x=\frac{14}{7} \\ x=2 \end{gathered}[/tex]then we substitute the value of x in the first equation in order to find y
[tex]3(2)+y=10[/tex]we isolate the y
[tex]\begin{gathered} y=10-6 \\ y=4 \end{gathered}[/tex]the solution is x=2, y=4