Question

How to find 5=x+2y -1=x+2y

Answer 1

Given the following System of equations:

`\begin{cases}x+2y=5 \\ x+2y=-1\end{cases}`

You can notice that the lines are parallel.

The Slope-Intercept form of the equation of a line is:

`y=mx+b`

Where "m" is the slope and "b" is the y-intercept.

In this case, if you solve for "y" from both equations of the system, you get:

- First equation:

`\begin{gathered} x+2y=5 \\ 2y=-x+5 \\ \\ y=-(1)/(2)x+(5)/(2) \end{gathered}`

Notice that the slope of the line is:

`m_1=-(1)/(2)`

- Second equation:

`\begin{gathered} x+2y=-1 \\ \\ y=-(1)/(2)x-(1)/(2) \end{gathered}`

Where the slope is:

`m_2=-(1)/(2)`

Since

`m_1=m_2`

The lines are parallel. By definition, when the lines are parallel there is no solution.

The answer is: No solutions exist.