Example Question - inconsistent system
Here are examples of questions we've helped users solve.
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.
Parallel Lines: Inconsistent System of Equations
The image shows two equations, which form a system of linear equations: 1) \( y = -\frac{5}{4}x + 8 \) 2) \( y = -\frac{5}{4}x - 9 \) To solve this system, we would normally look for values of \( x \) and \( y \) that satisfy both equations. However, if we compare the two equations, we can see that they both have the same slope, -5/4, but different y-intercepts. Since they both have the same slope, this means that the lines are parallel to each other. Parallel lines never intersect, which means that there is no solution to the system (they do not share any common points). In the context of systems of equations, this situation is known as an "inconsistent system."
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com