Given the following System of equations:
[tex]\begin{cases}x+2y=5 \\ x+2y=-1\end{cases}[/tex]You can notice that the lines are parallel.
The Slope-Intercept form of the equation of a line is:
[tex]y=mx+b[/tex]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:
[tex]\begin{gathered} x+2y=5 \\ 2y=-x+5 \\ \\ y=-\frac{1}{2}x+\frac{5}{2} \end{gathered}[/tex]Notice that the slope of the line is:
[tex]m_1=-\frac{1}{2}[/tex]- Second equation:
[tex]\begin{gathered} x+2y=-1 \\ \\ y=-\frac{1}{2}x-\frac{1}{2} \end{gathered}[/tex]Where the slope is:
[tex]m_2=-\frac{1}{2}[/tex]Since
[tex]m_1=m_2[/tex]The lines are parallel. By definition, when the lines are parallel there is no solution.
The answer is: No solutions exist.
