Question

Solve the system. Estimate the solution first. Enter whole numbers for the estimated solution andimproper fractions in simplest form for the algebraic solution.6x + y = 2x - 4y = 2The estimated solution isThe algebraic solution is

Answer 1

We need to solve the following system:

`\begin{cases}6x+y=2 \\ x-4y=2\end{cases}`

The first step we need to take is to multiply the first equation by 4.

`\begin{cases}24x+4y=8 \\ x-4y=2\end{cases}`

Then we have to add both equations:

`\begin{gathered} 25x=10 \\ x=(10)/(25) \end{gathered}`

Now we have to replace this value of x on the second equation:

`\begin{gathered} (10)/(25)-4y=2 \\ -4y=2-(10)/(25) \\ -4y=(50-10)/(25) \\ -4y=(40)/(25) \\ y=-(40)/(100) \end{gathered}`

The estimated solution is (10/25, -40/100). Now we need to simplify it:

`\begin{gathered} x=(10\colon5)/(25\colon5)=(2)/(5) \\ y=-(40\colon20)/(100\colon20)=-(2)/(5) \end{gathered}`

The algebraic solution is (2/5, -2/5)