We need to solve the following system:
[tex]\begin{cases}6x+y=2 \\ x-4y=2\end{cases}[/tex]The first step we need to take is to multiply the first equation by 4.
[tex]\begin{cases}24x+4y=8 \\ x-4y=2\end{cases}[/tex]Then we have to add both equations:
[tex]\begin{gathered} 25x=10 \\ x=\frac{10}{25} \end{gathered}[/tex]Now we have to replace this value of x on the second equation:
[tex]\begin{gathered} \frac{10}{25}-4y=2 \\ -4y=2-\frac{10}{25} \\ -4y=\frac{50-10}{25} \\ -4y=\frac{40}{25} \\ y=-\frac{40}{100} \end{gathered}[/tex]The estimated solution is (10/25, -40/100). Now we need to simplify it:
[tex]\begin{gathered} x=\frac{10\colon5}{25\colon5}=\frac{2}{5} \\ y=-\frac{40\colon20}{100\colon20}=-\frac{2}{5} \end{gathered}[/tex]The algebraic solution is (2/5, -2/5)
