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Can linear equations have the same Y?
If the two linear equations have the same slope (and the SAME y-intercept), the equations represent the same line. Since a line intersects with itself everywhere, there will be an infinite number of solutions (intersecting everywhere.)
What makes a linear system inconsistent?
A system of two linear equations can have one solution, an infinite number of solutions, or no solution. If a system has no solution, it is said to be inconsistent . The graphs of the lines do not intersect, so the graphs are parallel and there is no solution.
What are lines with the same y intercept?
If the y-intercepts are the same, the two equations represent the same line and there are INFINITELY MANY SOLUTIONS. 3b. If the y-intercepts are different, the two equations are distinct parallel lines and have NO SOLUTION.
Can 2 different linear functions have the same y-intercept?
Yes, two different linear functions can have the same y-intercept. To illustrate this, consider the following two linear functions: y = 2x + 5. y = 8…
Why must two parallel lines have different y-intercepts?
The slopes of the lines are the same and they have different y-intercepts, so they are not the same line and they are parallel. Two non-vertical lines are perpendicular if the slope of one is the negative reciprocal of the slope of the other.
When the system of equations have the same slope but different y-intercepts?
When lines have the same slope and different y-intercepts they are parallel lines. Parallel lines never intercept. Because these lines never intercept, they have no solution. Since they have no solution they are not consistent, dependent or independent like the last two systems we looked at.
Which equations are inconsistent?
Inconsistent equations of linear equations are equations that have no solutions in common. In this system, the lines will be parallel if the equations are graphed on a coordinate plane. Let’s consider an inconsistent equations as x – y = 8 and 5x – 5y = 25. They don’t have any common solutions.
Are parallel lines inconsistent?
Parallel lines never intersect, so they have no solutions. Since the lines are parallel, it is an inconsistent system.
Are two lines parallel if they have the same slope and y-intercept?
Parallel lines. We can determine from their equations whether two lines are parallel by comparing their slopes. If the slopes are the same and the y-intercepts are different, the lines are parallel.