Given the following System of equations:
[tex]\begin{cases}5x+3y=30 \\ 3x+3y=18\end{cases}[/tex]You can solve it using the Elimination Method. The steps are shown below:
1. You can multiply the first equation by -1
2. Add both equations.
3. Then solve for the variable "x".
Then:
[tex]\begin{gathered} \begin{cases}-5x-3y=-30 \\ 3x+3y=18\end{cases} \\ ----------- \\ -2x=-12 \\ \\ x=\frac{-12}{-2} \\ \\ x=6 \end{gathered}[/tex]4. Substitute the value of "x" into any original equation:
[tex]\begin{gathered} 3x+3y=18 \\ 3(6)+3y=18 \end{gathered}[/tex]5. Finally, solve for the variable "y". This is:
[tex]\begin{gathered} 18+3y=18 \\ 3y=18-18 \\ 3y=0 \\ y=0 \end{gathered}[/tex]The solution is:
[tex]\begin{gathered} x=6 \\ y=0 \end{gathered}[/tex]