The given system of equations is
[tex]\begin{gathered} y=3x+5\rightarrow(1) \\ 5x-2y=-7\rightarrow(2) \end{gathered}[/tex]
Substitute y in equation (2) by equation (1)
[tex]5x-2(3x+5)=-7[/tex]
Simplify the left side
[tex]\begin{gathered} 5x-2(3x)-2(5)=-7 \\ 5x-6x-10=-7 \end{gathered}[/tex]
Add the like terms on the left side
[tex]\begin{gathered} (5x-6x)-10=-7 \\ -x-10=-7 \end{gathered}[/tex]
Add 10 to both sides
[tex]\begin{gathered} -x-10+10=-7+10 \\ -x=3 \end{gathered}[/tex]
Divide both sides by -1
[tex]\begin{gathered} \frac{-x}{-1}=\frac{3}{-1} \\ x=-3 \end{gathered}[/tex]
Substitute x in equation (1) by -3 to find y
[tex]\begin{gathered} y=3(-3)+5 \\ y=-9+5 \\ y=-4 \end{gathered}[/tex]
The solution of the system of equations is {(-3, -4)}
Since the system has only one solution then it is an independent consistent system.
