Respuesta :
We have the following system of equations:
[tex]\begin{gathered} y=3x-2\ldots(A) \\ y=-2x+8\ldots(B) \end{gathered}[/tex]Solving by substitution method.
By substituting equation B into A, we have
[tex]-2x+8=3x-2[/tex]Now, by adding 2x to both sides, we get
[tex]8=5x-2[/tex]and by adding 2 to both sides, we get
[tex]\begin{gathered} 10=5x \\ or\text{ equivalently,} \\ 5x=10 \end{gathered}[/tex]Then, by dividing both sides by 5, x is given by
[tex]\begin{gathered} x=\frac{10}{5} \\ x=2 \end{gathered}[/tex]In order to find y, we can substitute this result into equation (A). It yields,
[tex]\begin{gathered} y=3(2)-2 \\ y=6-2 \\ y=4 \end{gathered}[/tex]Therefore, the solution of the system is x=2 and y=4.
