Question

Determine whether the given ordered pair is a solution of the system of the equation?

Answer 1

Given the system of equations :

`\begin{gathered} 2x-3y=4 \\ 2x+8y=11 \end{gathered}`

By subtract the first equation from the second equation :

`\begin{gathered} (2x+8y)-(2x-3y)=11-4 \\ (2x-2x)+(8y+3y)=7 \end{gathered}`
`\begin{gathered} 11y=7 \\ y=(7)/(11) \end{gathered}`

substitute with y at the first equation to find x

`\begin{gathered} 2x-3\cdot(7)/(11)=4 \\ 2x-(21)/(11)=4 \\ 2x=4+(21)/(11)=(65)/(11) \\ \\ x=(65)/(22) \end{gathered}`

So, the solution of the system is :

`\begin{gathered} x=(65)/(22) \\ \\ y=(7)/(11) \end{gathered}`