Question

Solve the following system of linear equations using elimination. 5x+3y=30 3x+3y=18

Answer 1

Given the following System of equations:

`\begin{cases}5x+3y=30 \\ 3x+3y=18\end{cases}`

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:

`\begin{gathered} \begin{cases}-5x-3y=-30 \\ 3x+3y=18\end{cases} \\ ----------- \\ -2x=-12 \\ \\ x=(-12)/(-2) \\ \\ x=6 \end{gathered}`

4. Substitute the value of "x" into any original equation:

`\begin{gathered} 3x+3y=18​ \\ 3(6)+3y=18​ \end{gathered}`

5. Finally, solve for the variable "y". This is:

`\begin{gathered} 18+3y=18 \\ 3y=18-18 \\ 3y=0 \\ y=0 \end{gathered}`

The solution is:

`\begin{gathered} x=6 \\ y=0 \end{gathered}`