Question

I need help on question 10.The solution of the system below is:3x + 2y = 143x – 2y = 10

Answer 1

Given the system of equations:

`\begin{cases}3x+2y=14 \\ 3x-2y=10\end{cases}`

We'll multiply the second equation by -1 and then add both equations up:

`\begin{gathered} \begin{cases}3x+2y=14 \\ 3x-2y=10\end{cases}\rightarrow\begin{cases}3x+2y=14 \\ -3x+2y=-10\end{cases} \\ \\ \rightarrow4y=4 \end{gathered}`

Solving the resulting equation for y ,

`\begin{gathered} 4y=4\rightarrow y=(4)/(4) \\ \\ \Rightarrow y=1 \end{gathered}`

We'll plug in this y-value in the first equation and solve for x ,

`\begin{gathered} 3x+2y=14 \\ \rightarrow3x+2(1)=14 \\ \rightarrow3x+2=14\rightarrow3x=12\rightarrow x=(12)/(3) \\ \\ \Rightarrow x=4 \end{gathered}`

Therefore, we can conclude that the solution to our system is:

`\begin{gathered} x=4 \\ y=1 \end{gathered}`