Question - Parallel Lines in a System of Linear Equations
Solution:
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.
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