Parallel Lines in a System of Linear Equations
This image shows two equations as part of a system of linear equations:
1. \( x + y = 2 \)
2. \( x + y = 3 \)
The instructions are to solve the system of linear equations by graphing and showing the solution on the provided coordinate system.
However, there's a notable issue with these equations: they represent parallel lines. The standard form for both equations is \( y = -x + b \), where \( b \) is the y-intercept. For the first equation, \( b = 2 \) and for the second equation, \( b = 3 \). This means that each line has the same slope but different y-intercepts.
Since they are parallel, they will never intersect. Therefore, this system of linear equations has no solution; it is inconsistent. If you were to graph these lines, you would draw two parallel lines that do not cross each other. The first line would intersect the y-axis at \( y = 2 \), and the second would intersect the y-axis at \( y = 3 \), both with a slope of -1.
