The given system of equations is
[tex]\begin{gathered} 3x+2y=4\rightarrow(1) \\ 5x+3y=7\rightarrow(2) \end{gathered}[/tex]Multiply equation (1) by -3 and equation (2) by 2 to make the coefficients of y equal in values and opposite in signs
[tex]\begin{gathered} -9x-6y=-12\rightarrow(3) \\ 10x+6y=14\rightarrow(4) \end{gathered}[/tex]Add equations (3) and (4) to eliminate y
[tex]\begin{gathered} (-9x+10x)+(-6y+6y)=(-12+14) \\ \\ x+0=2 \\ \\ x=2 \end{gathered}[/tex]The value of x is 2
